Gravitational PE Potential & Field — Practice Questions

Free NEET Physics multiple-choice questions on Gravitational PE Potential & Field. Attempt each question and reveal the answer with a full explanation.

The potential energy of a body of mass m at distance r from the center of Earth is given by U = - GMm r . The force acting on the body is: - GMm r 2 r GMm r 2 r - GMm r r GMm r r Kepler's second law states that the straight line joining the planet and the sun sweeps out equal areas in equal intervals of time. This law is a consequence of the conservation of: Angular momentum Linear momentum Energy Mass A point mass m is placed inside a uniform spherical shell of mass M and radius R at a distance r ( r < R ) from the center. The gravitational force on the point mass is: Zero GMm R 2 GMm r 2 GMmr R 3 The gravitational field due to a uniform solid sphere of mass M and radius R at a distance r < R from the center is: Directly proportional to r Inversely proportional to r Inversely proportional to r 2 Zero If the mass of the Earth is M , its radius is R and the gravitational constant is G , then the work done in taking a body of mass m from the Earth's surface to infinity is: GMm/R GMm/2R 2GMm/R Zero The binding energy of a satellite of mass m in a circular orbit of radius r is: GMm/2r -GMm/2r GMm/r -GMm/r Which of the following is correct regarding the gravitational field intensity E inside a uniform thin spherical shell of radius R ? E = 0 for all points E increases linearly with distance from center E is constant but non-zero E decreases as 1/r 2 The binding energy of an object of mass m on the surface of Earth is: mgR 0.5 mgR 2 mgR -mgR What is the weight of a body of mass m at the center of the Earth? Zero mg Infinite mg/2 The gravitational potential energy of a system of three particles, each of mass m , placed at the vertices of an equilateral triangle of side L , is: - 3Gm 2 L - Gm 2 L - 3Gm 2 2L - 6Gm 2 L The kinetic energy of a satellite in its orbit is K . Its potential energy will be: -2K -K 2K -K/2 The change in potential energy when a mass m is moved from the Earth's surface to a height h is U . If h R , then U is approximately: mgh mgh 1 + h/R mgR zero If the gravitational field intensity at a point is given by E , then the work done in moving a mass m by a distance dx in the direction of the field is: -mEdx mEdx Edx/m -Edx/m The ratio of the gravitational potential energy of a satellite at a height h = R above the Earth's surface to its potential energy at a height h = 2R is: 3:2 2:3 4:9 9:4 A satellite is moving in a circular orbit around Earth with a speed v . If its mass is m , then its total energy is: - 1 2 mv 2 1 2 mv 2 -mv 2 3 2 mv 2 The dimensional formula for gravitational potential is: [M 0 L 2 T -2 ] [M 1 L 2 T -2 ] [M 0 L 1 T -2 ] [M -1 L 3 T -2 ] The potential energy of a body of mass m is U on the surface of Earth. Its potential energy at a height h = R from the surface will be: U/2 2U U/4 Zero If the gravitational potential at a point on the surface of a thin spherical shell is V , what is the potential at a point at a distance R/2 from the center? V V/2 2V Zero If the mass of a planet is M and its radius is R , the work done to move a unit mass from its surface to a distance 2R from the center is: GM 2R GM R 2GM R 3GM 2R The kinetic energy of a satellite in its orbit is K . The additional kinetic energy required for it to escape the Earth's gravitational field is: K 2K K/2 4K The gravitational field intensity at a distance r from the center of a uniform solid sphere of mass M and radius R is E . For r < R , E is proportional to: r 1/r 2 1/r r 2 The potential energy of a satellite of mass m in a circular orbit of radius r is U . What is its kinetic energy? -U/2 -U U/2 -2U The binding energy of a system consisting of two particles of mass m separated by distance r is: Gm 2/r -Gm 2/r Gm 2/2r -Gm 2/2r What is the value of gravitational potential at the surface of a planet of mass M and radius R ? -GM/R GM/R 2 -GM/R 2 -2GM/R If the gravitational potential at a distance r from a point mass M is V , the gravitational field E at that point is: -dV/dr V/r -V/r d 2V/dr 2 For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is - 1 2 2 2 1 2 Two satellites of earth, S 1 and S 2 are moving in the same orbit. The mass of S 1 is four times the mass of S 2 . Which one of the following statements is true? The potential energies of earth satellites in the two cases are equal. S 1 and S 2 are moving with the same speed. The kinetic energies of the two satellites are equal. The time period of S 1 is four times that of S 2 . A satellite is orbiting just above the surface of the earth with period T . If d is the density of the earth and G is the universal constant of gravitation, the quantity 3 Gd represents T T 2 T 3 T The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury? 124 earth days 88 earth days 225 earth days 172 earth days A satellite of mass m is orbiting the Earth at a height h from its surface. If R is the radius of the Earth and g is the acceleration due to gravity at the surface, the total energy of the satellite is: -mgR 2 / 2(R+h) mgR 2 / 2(R+h) -mgR 2 / (R+h) 2mgR 2 / (R+h) The work done to raise a mass m from the surface of the Earth to a height h , which is equal to the radius of the Earth R , is: 1 2 mgR mgR 2mgR 3 2 mgR Which of the following graphs represents the variation of gravitational potential ( V ) with distance ( r ) from the center of a hollow spherical shell of radius R ? Constant V from 0 to R , then increasing (less negative) towards 0 Linear increase from 0 to R , then constant Zero from 0 to R , then decreasing Hyperbolic increase from 0 to R , then linear A satellite of mass m is orbiting the earth (radius R ) at a height h from its surface. The total energy of the satellite in terms of g 0 (acceleration due to gravity at earth's surface) is: - mg 0R 2 2(R+h) mg 0R 2 2(R+h) - mg 0R 2 R+h - 2mg 0R 2 R+h What is the gravitational potential at the center of a uniform thin semi-circular wire of mass M and radius R ? - GM R - 2GM R - GM 2R - GM R Four particles each of mass m are placed at the corners of a square of side L . The gravitational potential at the center of the square is: -4 2 Gm/L -4Gm/L -Gm/L -2 2 Gm/L The change in potential energy when a body of mass m is raised to a height nR from the earth's surface ( R is radius of earth) is: n n+1 mgR n n-1 mgR nmgR n 2 n+1 mgR The gravitational potential in a region of space is given by V = (3x + 4y + 12z) J/kg . The magnitude of the gravitational field intensity at the origin (0, 0, 0) is: 13 N/kg 7 N/kg 19 N/kg 0 N/kg Three equal masses m are placed at the three corners of an equilateral triangle of side a . The force exerted by this system on another particle of mass m placed at the midpoint of one of the sides is: 4Gm 2 3a 2 Gm 2 a 2 3Gm 2 4a 2 Zero What is the gravitational potential at the center of the Earth if its mass is M and radius is R ? -1.5 GM R -0.5 GM R - GM R Zero The gravitational field in a region is given by E = (5 i + 12 j ) N/kg . The change in gravitational potential V B - V A if a particle is moved from A(0,0) to B(4,3) is: -56 J/kg 56 J/kg -17 J/kg 17 J/kg What is the work done in bringing four particles each of mass m from infinity to the vertices of a square of side a ? -(4 + 2 ) Gm 2 a -4 Gm 2 a - (2 + 1 2 ) Gm 2 a -5.41 Gm 2 a The gravitational potential at a point on the surface of a solid sphere of mass M and radius R is V . What is the potential at the center of the sphere? 1.5 V V 2 V 0.5 V Which of the following physical quantities has the same dimensions as the product of Gravitational constant G and mass M ? Velocity squared times distance Acceleration times mass Force times distance Work done What is the gravitational potential energy of a particle of mass m at a distance r from the center of a uniform spherical shell of mass M and radius R , where r < R ? -GMm/R -GMm/r 0 -3GMm/2R Two point masses m and M are initially separated by a distance r . How much work is done by an external agent to increase their separation to 3r ? 2GMm 3r GMm 3r 3GMm 2r GMm r At what distance from the center of Earth (radius R ) is the gravitational potential maximum? Infinity R 0 (Center) At the surface If the gravitational potential at the surface of Earth is V s , then the potential at the center of Earth is: 1.5 V s V s 0.5 V s 2 V s The gravitational potential at the center of an equilateral triangle of side a with three masses m at its vertices is: -3 3 Gm a -3 Gm a - 3 Gm a -6 Gm a Three identical particles each of mass m are placed at the vertices of an equilateral triangle of side L . The work done by an external agent to increase the side of the triangle to 2L is: 3Gm 2 2L 3Gm 2 L Gm 2 L 3Gm 2 4L The gravitational field at a distance R/2 from the center of a solid sphere of radius R and mass M is E 1 . The field at a distance 2R from the center is E 2 . The ratio E 1/E 2 is: 2 1 1/2 4 The gravitational potential energy of a body of mass m at a distance r from the center of the Earth is U . What is the weight of the body at this distance? |U|/r U/r 2 Ur U 2/r Three particles each of mass m are kept at the vertices of an equilateral triangle of side L . The gravitational potential at the center of the triangle is: -3 3 Gm L -3 Gm L - 3 Gm L -2 3 Gm L The work done to move a body of mass m from the surface of Earth to a height h = 3R is: 3 4 mgR 2 3 mgR 1 4 mgR 4 3 mgR What is the work done to move a mass m from the center of a uniform spherical shell of mass M and radius R to its surface? 0 GMm/R GMm/2R -GMm/R Two bodies of masses m and 9m are placed at a distance d apart. At what distance from mass m is the gravitational potential maximum? None of these (Potential is always negative) d/4 d/2 3d/4 The work done by the gravitational force of the Sun on a planet in a complete revolution in an elliptical orbit is: Zero Positive Negative Depends on eccentricity The work done in taking a body of mass m from the surface of Earth to a height equal to the radius R of Earth is W . The work done in taking it from height R to height 2R is: W/3 W/2 2W W The gravitational potential V at a point on the axis of a uniform thin ring of mass M and radius a at a distance x from its center is: -GM / a 2 + x 2 -GM / (a + x) -GM / x -GMx / (a 2 + x 2) 3/2 The gravitational field in a region is given by E = (10 i + 10 j ) N/kg . The work done in moving a particle of mass 2 kg from (0,0) to (1 m , 1 m ) is: -40 J 40 J -20 J 20 J The gravitational field intensity E at a point on the axis of a uniform thin ring of mass M and radius a at a distance x from its center is given by: E = GMx (x 2 + a 2) 3/2 E = GMx (x 2 + a 2) 1/2 E = GM (x 2 + a 2) E = GMa (x 2 + a 2) 3/2 The gravitational field intensity at a distance r = R/4 from the center of a uniform solid sphere of mass M and radius R is: GM 4R 2 GM 16R 2 GM R 2 4GM R 2 For a uniform solid sphere of mass M and radius R , the ratio of the gravitational potential at the surface to the gravitational potential at the center is: 2:3 3:2 1:1 1:2 Four identical particles of mass m are placed at the corners of a square of side a . The total gravitational potential energy of the system is: - (4 + 2 ) Gm 2 a - 4 Gm 2 a - 2 Gm 2 a - (2 + 2 ) Gm 2 a The work done to increase the height of a body of mass m from h 1 = 0 to h 2 = R/2 is: mgR/3 mgR/2 mgR/4 2mgR/3 The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded are SAB. t 1 is the time for the planet to move from C to D and t 2 is the time to move from A to B then t 1=t 2 t 1>t 2 t 1=4t 2 t 1=2t 2 A satellite of mass m is in circular orbit of radius 3 ,R E about earth (mass of earth M E , radius of earth R E ). How much additional energy is required to transfer the satellite to a orbit of radius 9 ,R E ? GM Em 3R E GM Em 18R E 3GM Em 2R E GM Em 9R E The dimensional formula of the quantity GM/R (where G is gravitational constant, M is mass of Earth, R is radius) is same as that of: Square of speed Acceleration Force Energy The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are K A , K B and K C , respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then K B < K A < K C K A > K B > K C K A < K B < K C K B > K A > K C The escape velocity from the Earth's surface is v . The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is 2v 3v 4v v A particle of mass 'm' is projected with a velocity v = kV e (k < 1) from the surface of the earth. ( V e = escape velocity) The maximum height above the surface reached by the particle is R ( k 1+k ) 2 R 2k 1+k Rk 2 1-k 2 R ( k 1-k ) 2 The minimum energy required to launch a satellite of mass m from the surface of earth of mass M and radius R in a circular orbit at an altitude of 2R from the surface of the earth is: 5GmM 6R 2GmM 3R GmM 2R GmM 3R At what height from the surface of Earth the gravitation potential and the value of g are -5.4 10 7 J/kg and 6.0 m/s 2 respectively? (Take R = 6400 km ) 2600 km 1600 km 1400 km 2000 km A particle of mass M is situated at the center of a spherical shell of same mass and radius a . The gravitational potential at a point situated at a/2 distance from the center will be: -3GM/a -2GM/a -GM/a -4GM/a Two bodies of mass m and 4m are placed at a distance r . The gravitational potential at a point on the line joining them where the gravitational field is zero is: -9Gm/r -4Gm/r -6Gm/r -5Gm/r Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1 m , 2 m , 4 m , 8 m , ... from the origin. The resulting gravitational potential due to this system at the origin will be: -4G -G -2G -8G If the gravitational force had varied as r -5/2 instead of r -2 , the potential energy of a particle at a distance r from the center of Earth would be proportional to: r -3/2 r -2 r -1/2 r -5/2 The work done in shifting a particle of mass m from the center of Earth to the surface of Earth is (where M is mass of Earth and R is radius): GMm 2R 3GMm 2R GMm R Zero A body of mass m is taken from the Earth's surface to the height h = R , where R is the radius of the Earth. The increase in its potential energy is: 1 2 mgR mgR 1 4 mgR 2mgR A particle of mass M is placed at the center of a uniform spherical shell of equal mass M and radius R . The gravitational potential at a point P at a distance R/2 from the center is: -3GM/R -2GM/R -GM/R -4GM/R Which of the following graphs correctly represents the variation of gravitational potential V with distance r from the center of a uniform solid sphere of radius R ? A downward parabola for r < R joining a 1/r curve for r > R A straight line through origin for r < R and 1/r 2 for r > R Constant for r < R and 1/r for r > R A straight line for all r Two bodies of masses M 1 and M 2 are kept separated by a distance d . The potential at the point where the gravitational field is zero is: - G d ( M 1 + M 2 ) 2 - G d (M 1 + M 2) - G d ( M 1 - M 2 ) 2 Zero Two particles of masses m 1 and m 2 are initially at rest at infinite distance. They move towards each other under mutual gravitational attraction. At the instant when the distance between them is r , their relative velocity of approach is: 2G(m 1+m 2) r 2Gm 1m 2 (m 1+m 2)r G(m 1+m 2) r 2Gm 1 r The gravitational potential V at a distance r from the center of a solid sphere of radius R and mass M (for r R ) is given by: -GM(3R 2 - r 2) / (2R 3) -GM(R 2 - r 2) / (2R 3) -GM/R -3GM/2R The gravitational field intensity at the center of a uniform semi-circular wire of linear mass density and radius R is: 2G / R G / R G / R Zero A body is dropped from a height h = R into a tunnel bored through the center of the Earth. The velocity of the body at the center of the Earth is: 2gR gR 1.5gR 2.5gR At what height above the Earth's surface is the gravitational potential equal to -5.4 10 7 J/kg and the acceleration due to gravity is 6.0 m/s 2 ? (Take R = 6400 km) 2600 km 1600 km 3200 km 6400 km The ratio of the gravitational field at the center of a solid hemisphere of mass M and radius R to the field at its surface is: 3/8 1/2 1/4 3/4 The magnitude of the gravitational field intensity at the center of a uniform solid hemisphere of mass M and radius R is: 3GM 8R 2 GM 2R 2 3GM 4R 2 Zero The potential energy of a satellite of mass m and revolving at a height R above the surface of Earth (radius R , mass M ) is: - GMm 2R - GMm R GMm 2R - 2GMm R