Centre of Mass & System of Particles — Practice Questions

Free NEET Physics multiple-choice questions on Centre of Mass & System of Particles. Attempt each question and reveal the answer with a full explanation.

Two bodies of mass 1 kg and 3 kg have position vectors i + 2 j + k and -3 i - 2 j + k respectively. The center of mass of this system has a position vector: -2 i - j + k -2 i + 2 j + k -2 i - j - k i + j + k The center of mass of a solid cone of height h from its base lies on the axis of symmetry at a distance of: h/4 h/3 h/2 2h/3 A solid sphere, a hollow sphere and a disc, all of same mass and radius, are placed at the top of an incline and released. Which one will have the maximum kinetic energy at the bottom? All will have same kinetic energy Solid sphere Hollow sphere Disc The center of mass of a system of two particles of masses m 1 and m 2 is at a distance r 1 from m 1 and r 2 from m 2 . Then: m 1 r 1 = m 2 r 2 r 1 r 2 = m 1 m 2 m 1 r 2 = m 2 r 1 r 1 r 2 = m 1 m 2 Two masses m 1 and m 2 are connected by a spring of spring constant k and are placed on a smooth horizontal surface. If a force F is applied to m 1 in the horizontal direction, the acceleration of the center of mass of the system is: F / (m 1 + m 2) F / m 1 F / m 2 Zero A square plate of side L is in the xy -plane with one corner at the origin and sides along the axes. The distance of its center of mass from the origin is: L 2 L 2 L 2 L A uniform rod of length L and mass M is lying on a smooth horizontal table. A horizontal force F is applied at one end of the rod perpendicularly. The acceleration of the center of mass of the rod is: F/M 2F/M 3F/M 6F/M Two bodies of mass 1 kg and 3 kg have position vectors i +2 j + k and -3 i -2 j + k , respectively. The centre of mass of this system has a position vector : - i + j + k -2 i +2 k -2 i - j + k 2 i - j -2 k Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass. The centre of mass of the system from the 5 kg particle is nearly at a distance of : 50 cm 67 cm 80 cm 33 cm Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the center of mass of the system from the 10 kg mass is 20 3 m 10 m 5 m 10 3 m Three masses 2 kg , 4 kg and 6 kg are placed at the vertices of an equilateral triangle of side 1 m . If the 2 kg mass is at the origin (0,0) and the 4 kg mass is on the x-axis, the coordinates of the center of mass of the system are: ( 7 12 , 3 4 ) m ( 5 12 , 3 4 ) m ( 3 4 , 7 12 ) m ( 1 3 , 1 3 ) m Two particles of masses m 1 and m 2 are separated by a distance d . If the distance of m 1 from the center of mass is d 1 , then d 1 is given by: m 2 d m 1 + m 2 m 1 d m 1 + m 2 m 2 d m 1 m 1 d m 2 The center of mass of a system of three particles of masses 1 g , 2 g and 3 g is at (2, 2, 2) . Where should a fourth particle of mass 4 g be placed so that the center of mass of the whole system is at (0, 0, 0) ? (-3, -3, -3) (3, 3, 3) (2, 2, 2) (1, 1, 1) The center of mass of a uniform solid hemisphere of radius R is located at a distance h from its flat base along the axis of symmetry. The value of h is: 3R/8 R/2 4R/3 2R/3 A uniform rod of length L is standing vertically on a smooth horizontal surface. If the rod is slightly disturbed and it falls, the trajectory of the center of mass of the rod will be: A vertical straight line A parabola A circle An ellipse A thin uniform rod of length l and mass m is swinging as a vertical pendulum about its one end. The maximum angular velocity of the rod is . The maximum height to which the center of mass of the rod rises with respect to its lowest position is: l 2 2 6g l 2 2 3g l 2 2 2g l 2 2 12g Two thin uniform rods A and B of the same material and same cross-section but of lengths L and 2L are joined to form an L-shape. The center of mass of this system from the joint is at a distance of: 17 6 L 5 2 L 5 6 L 3 4 L When a body is in pure rolling on a stationary horizontal surface, the work done by the force of friction is: Zero Always positive Always negative Depends on the direction of motion A thin rod of length L has a linear mass density that varies as (x) = kx , where x is the distance from one end. The distance of the center of mass from that end is: 2 3 L 1 2 L 3 4 L 1 3 L Three point masses m, 2m, 3m are placed at the corners of an equilateral triangle of side a . The work done in moving the masses to the corners of an equilateral triangle of side 2a is: 11Gm 2 2a 11Gm 2 a 11Gm 2 4a Zero What is the work done by the force of friction on a body in pure rolling motion on a fixed horizontal surface? Zero Positive Negative Depends on the shape of the body An L-shaped object is made by joining two uniform rods of length L and mass M each. The object is placed in the xy -plane such that one rod lies along the x-axis (from x=0 to x=L ) and the other lies along the y-axis (from y=0 to y=L ). The coordinates of the center of mass of the object are: ( L 4 , L 4 ) ( L 2 , L 2 ) ( L 3 , L 3 ) ( L 6 , L 6 ) Two masses m and 9m are placed at a distance R . The distance of the center of mass of the system from the mass m is: 0.9R 0.1R 0.5R R/9 A circular disc of radius R is removed from a larger uniform circular disc of radius 2R such that the circumference of the smaller disc passes through the center of the larger disc and touches its outer edge. The center of mass of the remaining part is at a distance from the center of the large disc equal to: R/3 R/2 R/4 R/6 A T-shaped object is constructed by joining two identical uniform thin rods, each of mass M and length L . If one rod lies along the x-axis (from x=0 to x=L ) and the second rod is attached at the center of the first rod extending along the positive y-direction, the coordinates of the center of mass are: ( L 2 , L 4 ) ( L 2 , L 2 ) ( L 4 , L 2 ) ( L 2 , L 3 ) A uniform semi-circular lamina of radius R has its center of mass at a distance h from the center of its diameter. The value of h is: 4R 3 2R 3R 4 R 2 A uniform wire is bent into the shape of a quarter-circular arc of radius R . The distance of its center of mass from the center of the circle is: 2 2 R / 2R / 2 R / R / A point P on the rim of a wheel of radius R is initially in contact with the ground. The wheel rolls without slipping on a horizontal surface. After the wheel has completed half a revolution, the displacement of point P is: R 2 + 4 R 2R R 2 + 1 Three point masses 1 kg , 1.5 kg and 2.5 kg are placed at the vertices of an equilateral triangle of side 1 m . The 1 kg mass is at (0,0) and the 1.5 kg mass is at (1,0) . The y -coordinate of the center of mass is: 3 4 m 3 2 m 1 2 m 1 4 m Two particles of masses 2 kg and 3 kg have velocities 4 i + 2 j and x i - j respectively. If the velocity of their center of mass is 2 i + 0.2 j , the value of x is: 0.66 1.5 2.5 4.0 A system consists of four particles of masses m, 2m, 3m and 4m located at the corners of a square of side a in the xy -plane. If the mass m is at (0,0) , 2m at (a,0) , 3m at (a,a) and 4m at (0,a) , the distance of the center of mass from the origin is: a 10 29 a 2 2 3a 5 a 10 A solid sphere and a hollow sphere of the same mass and same radius roll down an inclined plane without slipping. They start from the same height. Which one has more total kinetic energy at the bottom? Both have the same Solid sphere Hollow sphere Depends on the angle of inclination A small disc of radius r is cut from a larger uniform disc of radius R ( R = 3r ). The center of the small disc is at a distance 2r from the center of the large disc. The center of mass of the remaining part is at a distance x from the center of the large disc. The value of x is: r/4 r/8 r/3 2r/9 The center of mass of a system of particles does NOT depend upon: Forces acting on the particles Masses of the particles Position of the particles Relative distance between particles A circular ring of mass 6 kg and radius a is placed such that its center is at the origin. Two particles of masses 2 kg and 3 kg are placed at (a, 0) and (0, a) respectively. The x -coordinate of the center of mass of the system is: 2a/11 3a/11 a/2 a/5 Point masses m 1 and m 2 are placed at the opposite ends of a rigid rod of length L , and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity 0 is minimum, is given by: x = m 2 L m 1 + m 2 from m 1 x = m 1 L m 1 + m 2 from m 1 x = L 2 from m 1 x = m 2 L m 1 from m 1 A particle of mass m is projected with velocity v at an angle of with the horizontal. The magnitude of the angular momentum of the particle about the point of projection when the particle is at its maximum height is: mv 3 2 2g mv 3 2 g mv 3 2 2g mv 3 2g A rod of length L has a non-uniform linear mass density given by = kx 2 , where x is the distance from one end. The distance of the center of mass from this end is: 3 4 L 2 3 L 1 2 L 4 5 L A square plate of side l and mass m has a small square of side l/2 removed from one corner. The center of mass of the remaining portion is at a distance d from the center of the original square. The value of d is: 2 l 12 l 12 2 l 6 l 6 A particle of mass m is projected with velocity v at an angle of 45 with the horizontal. The magnitude of the torque on the particle about the point of projection when the particle is at its maximum height is: mv 2 2 2 mv 2 2 mv 2 Zero A rod of length L has linear mass density which varies as = A + Bx where x is the distance from one end. The distance of the center of mass of the rod from this end (x=0) is: L(3A + 2BL) 3(2A + BL) L(2A + 3BL) 3(2A + BL) L(3A + BL) 2(2A + BL) L(A + 2BL) 3(2A + BL) Two bodies of masses n M and M are attached to the two ends of a light rod of length L . The moment of inertia of the system about an axis perpendicular to the rod and passing through the center of mass is: ( n n+1 )ML 2 ( n 2 n+1 )ML 2 ( 1 n+1 )ML 2 nML 2 A uniform rod of length L has linear mass density = 0(1 + x L ) where x is the distance from one end. The center of mass of the rod is at a distance from that end equal to: 5L 9 2L 3 L 2 4L 7 A uniform thin rod of mass M and length L is held at an angle with the vertical and released from rest with one end on a smooth horizontal floor. The velocity of the center of mass when the rod becomes horizontal is: 3gL 4 gL 1 2 gL 2gL(1- ) For a rigid body, if the net external force is zero, the center of mass: Must move with constant velocity Must be at rest May move with constant velocity or be at rest Must accelerate A circular disc of mass M and radius R has a small circular hole of radius R/4 with its center at a distance R/2 from the center of the disc. The distance of the center of mass of the remaining part from the center of the original disc is: R/30 R/15 R/12 R/20 Two bodies of masses 2 kg and 4 kg are moving with velocities 2 i and 10 i m/s respectively. The velocity of their center of mass is: 22 3 i m/s 6 i m/s 8 i m/s 7 i m/s Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the center of mass of the system from the 10 kg mass is: 20 3 m 10 3 m 5 m 5 3 m The center of mass of a system of three particles of masses 1 kg , 2 kg and 3 kg is located at (1, 1, 1) . If another particle of mass 4 kg is placed at the origin, the new center of mass is: (0.6, 0.6, 0.6) (0.5, 0.5, 0.5) (0.4, 0.4, 0.4) (1, 1, 1) The position of center of mass of a uniform semi-circular wire of radius R from its geometric center along the axis of symmetry is: 2R 4R 3 R 3R 4