Free NEET Physics multiple-choice questions on Motion in a Plane. Attempt each question and reveal the answer with a full explanation.
The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is: = -1 (4) = 45 = -1 (1/4) = 60 The angular speed of a flywheel making 120 revolutions per minute is: 4 rad/s 2 rad/s 120 rad/s rad/s A particle moves in a plane with a constant acceleration a = a x i + a y j . If its initial velocity is u = u x i , the equation of its path will be of the form: y = ax 2 + bx y = ax + b x 2 + y 2 = r 2 y = ax 2 A stone is dropped into a well 44.1 m deep. The sound of the splash is heard 3.13 s after the stone is dropped. The velocity of sound is: 339.2 m/s 330 m/s 343 m/s 320 m/s A particle moves in a circular path of radius 10 m with a constant speed of 20 m/s . The change in velocity when it covers an angle of 60 is: 20 m/s 20 3 m/s 10 m/s 0 A body is projected at such an angle that the horizontal range is three times the maximum height. The angle of projection is: -1 (4/3) -1 (3/4) 30 60 The average velocity of a projectile for its entire flight (from projection to landing on the same horizontal plane) is: u u u 0 A body is thrown horizontally with a velocity 2gH from the top of a tower of height H . It strikes the ground at a horizontal distance x from the foot of the tower, where x is: 2H H 2 H 4H A projectile is fired with speed u at angle with the horizontal. The speed of the projectile when its direction of motion makes an angle with the horizontal is: u u u u A particle of mass m is projected with velocity v at an angle 60 with the horizontal. When the particle is at its maximum height, the change in its velocity vector relative to its initial velocity is: v 60 downwards v 60 horizontal v vertical Zero A projectile is thrown with an initial velocity of u at an angle with the horizontal. The radius of curvature of its trajectory at the maximum height is: u 2 2 g u 2 2 g u 2 g u 2 g A particle has an initial velocity of 2 i + 3 j and acceleration of 0.3 i + 0.2 j . The magnitude of its displacement after 10 seconds is: 50 m 35 m 40 m 10 m A point moves on a circular track of radius r such that the distance covered s is s = ct 3 , where c is a constant. The tangential acceleration of the point is: 6ct 3ct 2 6c c/r If a particle moves with a velocity v = 3 i + 4x j , where x is its x -coordinate, the trajectory of the particle is a: Parabola Straight line Circle Ellipse A stone is thrown at an angle to the horizontal. If its horizontal range is R , then the maximum height H is related to R by the relation: 4H = R H = R 2H = R 4H = R The angular speed of the hour hand of a clock (in rad/s ) is: 21600 43200 3600 60 The speed of a particle moving in a circle of radius r varies with distance s as v = k s , where k is a constant. The centripetal acceleration of the particle is: k 2 s / r k 2 / r ks / r k / r A particle moves along a curve y = x 2 . When the particle is at (1, 1) , its x -component of velocity is 3 m/s . The y -component of its velocity at this instant is: 6 m/s 3 m/s 9 m/s 1 m/s A particle moves in a circle of radius 20 cm with a constant tangential acceleration. If the velocity of the particle is 80 cm/s at the end of the second revolution after motion has begun, the tangential acceleration is: 40 / cm/s 2 40 cm/s 2 640 cm/s 2 160 cm/s 2 A car moves on a circular path of radius R . At a certain instant, its speed is v and it is increasing at a rate a . The magnitude of the net acceleration is: a 2 + (v 2/R) 2 a + v 2/R v 2/R a - v 2/R The power delivered by gravity to a projectile during its upward journey: Is negative Is positive Is zero Changes from positive to negative A ball is thrown from the top of a tower with an initial velocity u = 10 i + 10 j m/s . The magnitude of its velocity after 2 seconds is: (Take g = 10 m/s 2 downward along negative y -axis) 10 2 m/s 20 m/s 10 5 m/s 10 m/s For a projectile, the ratio of the square of the time of flight to the maximum height is: 8/g 4/g 2/g g/8 A projectile is fired at an angle of 45 with the horizontal. If its speed at the maximum height is v , then its speed of projection was: 2 v v/ 2 2v v A projectile is fired from the origin with velocity v = (v 1 i + v 2 j ) . If the range of the projectile is twice the maximum height, then: v 2 = v 1 v 2 = 2v 1 v 1 = 2v 2 v 1 = v 2 A particle moves in a circle of radius 2 m with its speed increasing at a constant rate of 3 m/s 2 . If at t=0 the particle is at rest, the magnitude of its total acceleration at t=2 s is: 18.2 m/s 2 15.0 m/s 2 21.5 m/s 2 3.0 m/s 2 The equation of trajectory of a projectile is y = 3 x - 5x 2 . The angle of projection is: 60 30 45 90 A particle moves in a circle of radius R such that its displacement s = t 3 . The ratio of its tangential to centripetal acceleration at time t is: R 3t 3 2R 3t 4 3t 2 R R t 2 The speed of a projectile at its maximum height is 3 /2 times its initial speed u . The horizontal range of the projectile is: 3 u 2 2g u 2 2g 3u 2 g 3 u 2 g A car moves on a circular track of radius 250 m with a speed that increases at the rate of 0.5 m/s 2 . At the instant when its speed is 25 m/s , the magnitude of its net acceleration is: 2.55 m/s 2 2.50 m/s 2 3.00 m/s 2 0.50 m/s 2 A particle moves in a circle of radius r . The angular displacement (in radians) varies with time t as = 2t 2 . The ratio of its centripetal acceleration to its tangential acceleration at any time t is: 4t 2 2t 2t 2 t A projectile is thrown with an initial velocity u = a i + b j . If the range of the projectile is twice its maximum height, then: b = 2a a = 2b b = a b = 4a A body is moving with a constant speed v in a circle of radius r . The magnitude of the change in velocity when it has turned through an angle of 120 is: 3 v v 2 v 2v A motor car is moving with a velocity of 20 m/s on a circular road of radius 100 m . If the brakes are applied to reduce the speed at the rate of 1 m/s 2 , what is the total acceleration of the car? 17 m/s 2 4 m/s 2 1 m/s 2 5 m/s 2 A bullet is fired from a gun at the speed of 280 m/s in the direction 30 above the horizontal. The maximum height attained by the bullet is ( g = 9.8 m/s 2, sin 30 = 0.5 ): 1000 m 2000 m 3000 m 4000 m A plane is flying horizontally at an altitude of 490 m with a speed of 360 km/h . A bag is released from the plane. The horizontal distance covered by the bag before hitting the ground is ( g=9.8 m/s 2 ): 1000 m 500 m 2000 m 100 m A particle moves in a circle of radius 5 cm with a constant speed and time period 0.2 s . The acceleration of the particle is: 5 m/s 2 25 m/s 2 36 m/s 2 15 m/s 2 A body is thrown vertically upwards with a velocity u . Find the distance travelled by it in the last second of its upward journey. g/2 u - g/2 g u/2 The displacement of the tip of the minute hand of a clock of length r in 20 minutes is: r 3 r 2r 3 2r A projectile is thrown with velocity u at angle with horizontal. The magnitude of its velocity at a height h is: u 2 - 2gh u 2 + 2gh u u - gt For a projectile, the ratio of maximum height H to the square of time of flight T 2 is ( g = 10 m/s 2 ): 5/4 5 10 1/4 If the range of a projectile is n times its maximum height, then the angle of projection is: -1 (4/n) -1 (n/4) -1 (4n) -1 (2/n) A particle moves in a circle of radius 25 cm at 2 revolutions per second. The acceleration of the particle in m/s 2 is: 4 2 2 8 2 2 2 A particle moves such that its position vector is r = t i + t j . The velocity of the particle is: Perpendicular to r Parallel to r Directly towards the origin Directed away from the origin A projectile is fired such that its kinetic energy at the highest point of its trajectory is 75 % of its initial kinetic energy. The angle of projection with the horizontal is: 30 45 60 15 The horizontal range of a projectile is R . If the initial velocity is kept same but the angle of projection is changed from 30 to 60 , the new horizontal range will be: R R/2 2R 3 R The position vector of a particle is given by r = a ( t) i + a ( t) j . The velocity of the particle is: Perpendicular to r Parallel to r Directed towards the origin Directed away from the origin A particle moves in a plane such that its coordinates are x = a t and y = b t . The trajectory of the particle is a/an: Ellipse Circle Straight line Parabola A bullet fired at an angle of 30 with the horizontal hits the ground 3 km away. By adjusting the angle of projection, the maximum range that can be reached (with same muzzle velocity) is: 2 3 km 6 km 3 3 km 4 km A bullet fired from a gun reaches a maximum height of 80 m and a horizontal range of 320 m . The angle of projection with the horizontal is: 45 30 60 -1 (1/2) A projectile is fired from the surface of the earth with a velocity of 5 ms -1 and angle with the horizontal. Another projectile fired from another planet with a velocity of 3 ms -1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in ms -2 ): ( g = 9.8 ms -2 ) 3.5 5.9 16.3 110.8 A particle moves so that its position vector is given by = cos ωt + sin ωt . Which of the following is true? Velocity is perpendicular to and acceleration is directed towards the origin Velocity and acceleration both are perpendicular to Velocity and acceleration both are parallel to Velocity is perpendicular to and acceleration is directed away from the origin A projectile is fired at an angle of 45 with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection is: -1 (1/2) 60 -1 ( 3 /2) 45 A particle starting from rest, moves in a circle of radius r . It attains a velocity of V 0 m/s in the n th round. Its angular acceleration will be: V 0 2 / 4πnr 2 V 0 / n V 0 2 / 4πnr V 0 2 / 4πr A body is projected with a velocity u such that its horizontal range is twice the maximum height. Its range is: 4u 2 / 5g u 2 / g 2u 2 / g u 2 / 2g For a particle in uniform circular motion, the acceleration a at a point P(R, ) on the circle of radius R is (here is measured from the x -axis): - v 2 R i - v 2 R j - v 2 R i + v 2 R j v 2 R i + v 2 R j - v 2 R i + v 2 R j A particle moves in a circular path of radius R such that its displacement s as a function of time t is s = t 2 . The centripetal acceleration at time t is: 4t 2/R 2t/R t 2/R 2/R The horizontal range R and the maximum height H of a projectile are related as R = 4 H 1H 2 , where H 1 and H 2 are maximum heights for two angles of projection that result in the same range R . If the angles are and (90 - ) , then R is equal to: 4 H 1H 2 2 H 1H 2 H 1H 2 16 H 1H 2 The ratio of the radii of curvature of the trajectory of a projectile at the point of projection and at the highest point is (angle of projection is ): 1/ 3 3 1/ 2 2 A particle moves in a plane with velocity v = a i + bx j , where i and j are unit vectors along x and y axes and a, b are constants. At t=0 , the particle is at (0,0) . The equation of its path is: y = b 2a x 2 y = b a x 2 y = bx y = 2a b x 2 The average velocity of a projectile between the point of projection and the highest point of its trajectory is (projection speed u , angle ): u 2 1 + 3 2 u u 2 1 + 2 2 u 2 1 + 2 A particle moves along a circle of radius R such that its position vector r makes an angle = t 2 with the x-axis. The magnitude of its acceleration at t = 1 s is: 2R 1+4t 4 4R 2R R 2 A body is projected horizontally from the top of a tower with a velocity of 10 m/s . The radius of curvature of its trajectory at t = 1 s is ( g = 10 m/s 2 ): 20 2 m 10 2 m 25 m 5 2 m A particle moves in the x-y plane with a constant acceleration g in the negative y-direction. Its equation of motion is y = ax - bx 2 , where a and b are constants. The x-component of its velocity is: g/2b g/b 2g/b a g/2b A projectile is fired from the ground with an initial velocity u at an angle with the horizontal. At what time t will the velocity vector be perpendicular to the initial velocity vector? u / (g sin ) u / (g cos ) u sin / g u tan / g A particle moves in a circle of radius R . If its tangential acceleration is equal to its centripetal acceleration, the time taken to complete the first revolution, starting from rest, is: √(4πR/a t) √(2πR/a t) 2πR/a t πR/a t A particle moves in a circle of radius R . Its linear speed is given by v = ct , where c is a constant. The angle between the velocity vector and the acceleration vector at time t is: -1 ( c t 2 R ) -1 ( R c t 2 ) -1 ( ct R ) 0 For a projectile motion, if the initial velocity is doubled without changing the angle of projection, the maximum height reached will: Increase by 4 times Double Increase by 8 times Remain same For a particle in uniform circular motion, the acceleration vector a at a point P(R, ) on a circle of radius R is: - v 2 R i - v 2 R j v 2 R i + v 2 R j - v 2 R i + v 2 R j - v 2 R i + v 2 R j A particle is moving with a constant speed v in a circle. What is the magnitude of average velocity after it has described an angle of 60 ? 3v v 3 v 2v A particle is projected from the ground with velocity u at an angle with the horizontal. The time at which the horizontal and vertical displacements are equal is: 2u( - ) g u( - ) g 2u g 2u g A bullet is fired from the ground at an angle . If the air resistance provides a constant retardation a in the horizontal direction, the horizontal range R is given by: 2u 2 g - 2u 2 a 2 g 2 u 2 2 g 2u 2 g + 2u 2 a 2 g 2 u 2 2 2g A particle moves along a circular path of radius R with a constant angular velocity . Its displacement after time t is: 2R ( t / 2) R t R ( t) 2R ( t / 2) A particle is moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle to the horizontal, the maximum height attained by it equals 4R . The angle of projection is then given by: = 2 2 R gT = R gT = 2 gT R = 2 R gT A ball is thrown vertically upward with a speed u . If it experiences a constant air resistance f that acts opposite to the direction of motion, what is the ratio of the time of ascent ( t a ) to the time of descent ( t d )? g-a g+a g+a g-a g-a g+a 1 A particle moves along a circular path of radius R such that the radial acceleration is a r = k 2 R t 2 . The tangential acceleration of the particle is: kR k 2 R t kR/t k 2 R A particle moves in the x-y plane with a constant acceleration a directed along the negative y -axis. The equation of motion is y = kx - mx 2 . The speed of the particle at the origin is: a(1+k 2) 2m a 2m ak m a m(1+k 2) A projectile is fired at an angle with the horizontal. The ratio of the radius of curvature at the point of projection to the radius of curvature at the maximum height is: 1/ 3 3 1/ 2 2 A bullet fired vertically upward from a gun returns to the starting point in 10 s . Its maximum height is ( g = 10 m/s 2 ): 125 m 500 m 250 m 100 m A body is projected with a velocity u at an angle . Its velocity is perpendicular to the initial velocity at time t equal to: u g u g 2u g u g A particle moves along a path y = x 2 2 with a constant speed v . The acceleration of the particle at the origin (0,0) is: v 2 v 2 2 2v 2 Zero A particle moves in a circle of radius r with a constant speed v . The magnitude of average acceleration during the time it covers one-fourth of the circle is: 2 2 v 2 / ( r) v 2 / r 2 v 2 / ( r) 4v 2 / ( r) The horizontal range of a projectile is R and the maximum height is H . If the angle of projection is , then the relation R 2 8H + H 2 represents: The radius of curvature at the highest point The initial velocity squared divided by g The total time of flight squared The radius of curvature at the point of projection A projectile is fired at an angle with the horizontal. If the horizontal range is R , what is the radius of curvature of its path at the point of projection? R / (2 2 ) R 2 / g R / (2 ) R A particle moves with constant speed v along a circle of radius r . The average velocity during a time interval in which it turns through an angle is: (2v/ ) ( /2) v ( /2) (v/ ) v ( /2) Two projectiles are thrown with the same initial velocity at angles and (90 - ) with the horizontal. The ratio of their maximum heights is: 2 : 1 : 1 : 1 : 1 A body is projected with a velocity u at an angle of 60 with the horizontal. Its velocity at the maximum height is: u/2 u u 3 /2 0 A particle moves along a circle of radius R . The distance and displacement of the particle after covering three-fourths of the circle is: 3πR/2, √2R 3πR/2, 2R πR, R πR/2, √2R A particle moves in a plane with a constant acceleration in a direction different from the initial velocity. The path of the particle is a/an: Parabola Circle Ellipse Straight line The angular displacement of a particle moving in a circular path is given by = t 3/20 + t 2/4 where is in radians and t is in seconds. The angular velocity of the particle at t = 2 s is: 1.3 rad/s 0.8 rad/s 2.5 rad/s 3.0 rad/s A projectile is thrown with an initial kinetic energy K . If it is thrown at an angle of 45 with the horizontal, its kinetic energy at the highest point will be: K/2 K/ 2 K Zero A person can throw a ball to a maximum horizontal distance of 80 m . The maximum height to which he can throw the same ball vertically is: 40 m 80 m 20 m 160 m A bullet is fired from a height of 10 m with a horizontal velocity of 100 m/s . The distance from the foot of the tower where it strikes the ground is ( g=10 m/s 2 ): 141.4 m 100 m 200 m 50 m The maximum height attained by a projectile is 25 m and its horizontal range is 100 m . The angle of projection is: 45 30 60 tan -1 (2) Two stones are thrown with same speed u at angles (45 + ) and (45 - ) with the horizontal. The ratio of their horizontal ranges is: 1 : 1 1 : 2 2 : 1 : 1 For a projectile, the ratio of maximum height to horizontal range is 1/4 . The angle of projection is: 45 30 60 75 A projectile is fired at an angle of 30 with the horizontal. Its vertical component of velocity at the highest point is: 0 u 30 u 30 u A bullet is fired from a gun at 30 above the horizontal. Its horizontal range is 100 m. If the muzzle velocity remains same, its range at 60 will be: 100 m 200 m 50 m 150 m A projectile is fired at an angle of 30 to the horizontal such that the vertical component of its initial velocity is 80 m/s . Its time of flight is: ( g = 10 m/s 2 ) 16 s 8 s 32 s 4 s A particle moves in a circular path with constant speed. The angle between its velocity vector and acceleration vector is: 90 0 180 45 For angles of projection of a projectile at angles (45 - ) and (45 + ) , the horizontal ranges described by the projectile are in the ratio of: 1 : 1 2 : 3 1 : 2 2 : 1 A person can throw a ball to a maximum horizontal distance R . The maximum height to which he can throw the same ball is: R/2 R 2R R/4 A ball is projected with kinetic energy K at an angle of 45 to the horizontal. At the highest point, its kinetic energy is: K/2 K Zero K/ 2 The horizontal range of a projectile is maximum when the angle of projection is: 45 30 60 90 A body is projected at an angle of 30 with the horizontal. The ratio of its horizontal velocity to the velocity at the highest point is: 1:1 3 :2 2:1 1:2 The coordinates of a particle at any time t are given by x = At 2 and y = Bt 2 . The speed of the particle is: 2t A 2 + B 2 t A 2 + B 2 A 2 + B 2 2t(A + B) A particle moves along a circular path of radius R . If its speed is tripled and its radius is doubled, the centripetal acceleration will change by a factor of: 4.5 9 1.5 6 A body is projected with a velocity u at an angle with the horizontal. The time after which its vertical velocity becomes zero is: u / g u / g u / g 2u / g The angular speed of the second hand of a watch is: / 30 rad/s / 60 rad/s rad/s 2 rad/s A projectile is thrown with an initial velocity (6 i + 8 j ) m/s . If g = 10 m/s 2 , then its horizontal range is: 9.6 m 4.8 m 12 m 19.2 m The x and y coordinates of a particle at any time t are given by x = 7t + 4t 2 and y = 5t , where x and y are in m and t in s. The acceleration of the particle at 5 s is: 8 m/s 2 20 m/s 2 40 m/s 2 Zero A body is whirled in a horizontal circle of radius 20 cm . It has an angular velocity of 10 rad/s . What is its linear velocity at any point of circular path? 2 m/s 20 m/s 10 m/s √ 2 m/s A particle moves in a circle of radius 25 cm at two revolutions per second. The acceleration of the particle in m/s 2 is: 4π 2 π 2 8π 2 2π 2 At the uppermost point of a projectile's path, its velocity and acceleration are: Perpendicular to each other Parallel to each other At an angle of 45 to each other In opposite directions The ratio of the angular speed of the second hand to the minute hand of a clock is: 60 : 1 1 : 60 12 : 1 3600 : 1 A stone is thrown with a velocity u at an angle with the horizontal. Its horizontal range is maximum when is: 45 30 60 90 The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is: 60 15 30 45 A particle moves in a circular path of radius r . In half a period of revolution, its displacement and distance covered are: 2r, r r, 2r 2r, 2 r 0, r A particle moves in a circle of radius 5 cm with constant speed and time period 0.2π s . The acceleration of the particle is: 5 m/s 2 15 m/s 2 25 m/s 2 36 m/s 2 If the range of a projectile is 4 times its maximum height, the angle of projection is: 45 30 60 0 A person can throw a ball to a maximum horizontal distance of 100 m . The maximum vertical height to which he may throw the same ball with the same speed is: 50 m 100 m 200 m 25 m A ball is projected horizontally from the top of a tower with a velocity of 10 m/s. The velocity of the ball after 1 second will be ( g = 10 m/s 2 ): 10 2 m/s 10 m/s 20 m/s 0 m/s The maximum range of a gun on horizontal terrain is 16 km. If g = 10 m/s 2 , what must be the muzzle velocity of the bullet? 400 m/s 200 m/s 160 m/s 800 m/s If a particle moves with a constant speed in a vertical circle, then its: Acceleration is not constant Velocity is constant Acceleration is constant None of these An object is projected at an angle of 45 with the horizontal. The kinetic energy of the object at the highest point is: 0.5 E E Zero 0.25 E A particle moves along a circular path of radius R . The distance and displacement of the particle when it completes one and a half revolutions are respectively: 3 R and 2R 2 R and R 3 R and zero R and 2R For a particle in uniform circular motion, if the radius is doubled and the frequency is halved, the centripetal acceleration will: Be halved Be doubled Remain unchanged Be quadrupled The range of a projectile when fired at 15 is 50 m . If it is fired with the same speed at 45 , its range will be: 100 m 75 m 150 m 200 m At what angle with the horizontal should a projectile be fired so that its maximum height is equal to its horizontal range? -1 (4) 45 -1 (2) 60 A particle moves in the x-y plane with coordinates x = a sin ωt and y = a cos ωt . The speed of the particle is: aω aω 2 ω sin ωt ω The velocity of a projectile at the initial point A is (2 + 3) m/s . Its velocity (in m/s ) at point B (the end of the flight on the horizontal plane) is: 2 - 3 -2 - 3 -2 + 3 2 + 3 A projectile is fired at 30 with the horizontal. Which of the following graphs best represents the vertical component of velocity ( v y ) versus time ( t )? A straight line with a negative slope crossing the time axis A straight line with a positive slope passing through origin A parabola opening downwards A horizontal straight line A projectile is thrown with kinetic energy K at an angle of 60 with the horizontal. Its kinetic energy at the highest point of its trajectory will be: K/4 K/2 K/8 Zero A particle moves along a path such that its position vector is r = t 2 i + 2t j . The equation of its trajectory is: y 2 = 4x x 2 = 4y y = x 2 x = y 2 For a projectile, the ratio of maximum height to the square of the time of flight is: g/8 g/4 g/2 2g A stone is thrown at an angle to the horizontal. Its path is y = x√3 - gx 2 2 . The angle of projection is: 60 30 45 0 Two bullets are fired horizontally and simultaneously from the same height from two guns with different speeds v 1 and v 2 ( v 1 < v 2 ). Which bullet will hit the ground first? Both will reach simultaneously Slower bullet Faster bullet Depends on their masses The horizontal range of a projectile is 4 3 times its maximum height. The angle of projection is: 30 45 60 90 Which of the following remains constant for a projectile fired from the earth's surface? Horizontal component of velocity Vertical component of velocity Kinetic energy Momentum The horizontal range of a projectile is R . If the initial velocity is doubled, keeping the angle of projection same, the new range will be: 4R 2R R/2 2 R A ball is thrown horizontally from the top of a cliff 20 m high. It hits the ground at a distance of 40 m from the foot of the cliff. The initial velocity of the ball is: ( g = 10 m/s 2 ) 20 m/s 10 m/s 40 m/s 5 m/s The angle of projection for which the horizontal range and maximum height of a projectile are equal is: -1 (4) -1 (2) 45 60 Two projectiles of same mass and with same velocity are thrown at 60 and 30 with the horizontal, then which of the following will remain the same? Horizontal Range Maximum Height Time of Flight Velocity at max height The x and y coordinates of the particle at any time are x = 5t - 2t 2 and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s is: -4 m/s 2 5 m/s 2 -2 m/s 2 0 m/s 2 A projectile is given an initial velocity of ( + 2) m/s , where is along the ground and is along the vertical. If g = 10 m/s 2 , the equation of its trajectory is: y = 2x - 5x 2 y = x - 5x 2 4y = 2x - 5x 2 4y = 2x - 25x 2 A particle of mass m is projected with velocity v making an angle of 45 with the horizontal. When the particle lands on the level ground, the magnitude of the change in its momentum will be: mv 2 Zero 2mv mv/ 2 A ball is thrown vertically upward. It has a speed of 10 m/s when it has reached one half of its maximum height. How high does the ball rise? (Take g = 10 m/s 2 ) 10 m 5 m 15 m 20 m A particle moves in the x-y plane according to rule x = a ωt and y = a(1 - ωt) . The path followed by the particle is: a circle a parabola a straight line an ellipse A projectile is fired with an initial velocity u at an angle with the horizontal. The magnitude of the change in velocity when it reaches the maximum height is: u u u Zero A particle moves in a circle of radius R with a constant speed v . The magnitude of the change in velocity when it covers an angle is: 2v ( /2) v 2v ( /2) v A ball is thrown at an angle and another ball is thrown at an angle (90 - ) with the horizontal from the same point with the same velocity u . The ratio of their maximum heights is: 2 2 2 1 : 1 A person aiming a rifle at a bird on a tree fires a bullet. The bird, seeing the flash, drops from the tree. The bullet will: Hit the bird Pass above the bird Pass below the bird Hit the bird only if the rifle is high velocity A particle moves with constant speed v along a circular path of radius r and completes the circle in time T . What is the average velocity of the particle during the time T/2 ? 2v v v 2 Zero Two particles are projected with the same speed but at different angles 45 + and 45 - . The ratio of their horizontal ranges is: 1:1 1:2 2 : 1 2 : 1 The coordinates of a moving particle at any time t are given by x = ct 2 and y = bt 2 . The speed of the particle at any time t is: 2t c 2 + b 2 2t(c + b) t c 2 + b 2 c 2 + b 2 A particle moves in a circular path of radius R with a constant angular velocity . Its velocity at any point P(R, ) is given by: R(- i + j ) R( i + j ) R( i - j ) R( i + j ) A stone is dropped from a height h . Simultaneously, another stone is thrown up from the ground which reaches a height 4h . The two stones will cross each other after a time: h/8g h/2g 2h/g h/g A particle moves with a velocity v = kt i + k j , where k is a constant. The equation of its path (trajectory) is: y = 2kx y = kx 2 y = x/k x = y 2 A point on the rim of a wheel of radius R is initially in contact with the ground. The wheel rolls forward through half a revolution. The magnitude of displacement of the point is: R 2 + 4 R 2R R 2 + 1 Two particles are projected from the same point with the same speed u at angles of projection and (90 - ) . If T 1 and T 2 are the times of flight in the two cases, then the horizontal range R is given by: R = 1 2 g T 1 T 2 R = g T 1 T 2 R = 2g T 1 T 2 R = 1 4 g T 1 T 2 A plane is flying horizontally at a height of 1960 m with a velocity of 360 km/h . When it is vertically above point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is: 2000 m 1000 m 4000 m 3200 m A ball is thrown from a point with a speed u at an angle of projection . From the same point and at the same instant, a person starts running with a constant speed u/2 to catch the ball. Will he be able to catch the ball if: = 60 = 30 = 45 Never possible A ball is thrown at an angle of 30 with the vertical. The ratio of its horizontal range to its maximum height is: 4/√3 4√3 √3/4 1/4 A body is projected with a velocity u at an angle to the horizontal. The radius of curvature of its trajectory at the point of projection is: u 2 / (g cos ) u 2 cos 2 / g u 2 / g u 2 sin 2 / g For a particle in uniform circular motion, the acceleration vector is directed: Towards the center along the radius Along the tangent to the circle Away from the center along the radius At an angle of 45 to the radius If the range of a projectile is R and the time of flight is T , the angle of projection is given by: tan = gT 2 / 2R tan = 2R / gT 2 tan = gT / R tan = R / gT An object moves in a circle of radius r at a constant speed v . The magnitude of average acceleration during a half-revolution is: 2v 2 / πr v 2 / r Zero v 2 / πr A projectile is fired from the ground with a speed u at an angle with the horizontal. The magnitude of the change in velocity between the point of projection and the highest point is: u u u u(1 - ) A ball is projected with a velocity 10 m/s at an angle of 60 with the vertical direction. Its speed at the highest point of its trajectory will be: 8.66 m/s 5 m/s 10 m/s Zero A particle moves in a circle of radius R . In one-fourth of a period of revolution, the ratio of the magnitude of its displacement to the distance covered is: 2 2 / 2 / /2 2 1/ A particle moves in a circle of radius 20 cm with a tangential acceleration of 5 cm/s 2 . If the speed of the particle is 10 cm/s at a certain instant, the magnitude of the total acceleration is: 5 2 cm/s 2 10 cm/s 2 5 cm/s 2 7.07 cm/s 2 For a projectile, the ratio of the kinetic energy at the highest point to the initial kinetic energy is 1/2 . The angle of projection is: 45 30 60 0 The trajectory of a projectile is y = 3 x - gx 2 2 . The angle of projection is: 60 30 45 0 A particle moves along a circular path of radius r . If it completes half a revolution, the magnitude of the average velocity is ( T is the time period): 4r/T r/T 2r/T 8r/T A projectile is thrown with an initial velocity of u i + v j . If the range of the projectile is double the maximum height, then: v = u v = 2u u = 2v u = v