Recent questions in System of Particles and Rotational Motion

A shell is projected from a level ground with a velocity of $20\;m/s$ at $45^{\circ}$ to the horizontal. When the shell is at highest point, it breaks into two equal fragments. One of the fragment whose initial velocity after the explosion is zero, falls vertically downward. At what distance from the point of projection does the other fragment fall? $(g=10\;ms^{-2})$

asked Nov 21, 2013 by meena.p

1 answer

A shell in flight explodes into n equal fragments. K of the fragments reach the ground earlier than the other fragments. The acceleration of their centre of mass subsequently will be

asked Nov 21, 2013 by meena.p

1 answer

A balloon of mass M is stationary in air. It has a ladder on which a man of mass m is standing. If the man starts climbing up the ladder with a velocity v relative to the ladder, the velocity of the balloon is

asked Nov 21, 2013 by meena.p

1 answer

Two blocks of masses 4 kg and 3 kg are placed on a friction less surface connected by a string. An external force gives a velocity 7 m/s to the heavier mass in the direction of the lighter , velocity of their centre of mass is

asked Nov 21, 2013 by meena.p

1 answer

Two particles of mass 2m and 3m are at a distance 'd' apart. Under their mutual gravitational force, they start moving towards each other. The acceleration of their center of mass when they are $d/2$ apart is

asked Nov 21, 2013 by meena.p

1 answer

Two bodies of masses 10 kg and 2 kg are moving with velocities $2m/s$ and $10m/s$, towards each other . The velocity of their centre of mass is

asked Nov 21, 2013 by meena.p

1 answer

A boy of mass 36 kg moves from one end to other end of a boat of mass 72 kg on still water. If the length of the boat is 2.7 m, the displacement of the boat is

asked Nov 21, 2013 by meena.p

1 answer

Two particles A and B of masses 2 kg and 3 kg are separated by 10 m. If they move towards each other under a mutual force of attraction, the distance of the point where they meet from the initial position of A is

asked Nov 21, 2013 by meena.p

1 answer

Three particles of masses 8 kg, 4 kg and 4 kg situated at $(4,1),(-2,2)$ and $(1,-3)m$ are acted upon by external forces $6 \hat {j},-6 \hat {i}$ and $14 \hat {i}\;N$ respectively . The acceleration of the center of Mass of the system is

asked Nov 21, 2013 by meena.p

1 answer

Two particles of masses 1 kg and 3 kg have velocities $(2 \hat i-3 \hat j+4 \hat k)ms^{-1}$ and $(4 \hat {i}+2 \hat j+\hat k)ms^{-1}$ at a given instant of time. The velocity of the center of mass is

asked Nov 21, 2013 by meena.p

1 answer

A uniform circular sheet has a radius r. A square sheet whose diagonal length is equal to the radius of the plate is removed. The maximum distance of the centre of mass of the square sheet from the center of original sheet is :

asked Nov 21, 2013 by meena.p

1 answer

A uniform metal rod is bent units L-shaped with the bent arms at 90 to each other. The distance of the center of mass of the remaining portion from the center of the original sheet is

asked Nov 21, 2013 by meena.p

1 answer

A uniform square sheet has a side of length $2R$. A circular sheet of maximum possible area is removed from one of the quadrants of the square sheet. The distance of the center of mass of the remaining portion from the center of the original sheet is

asked Nov 21, 2013 by meena.p

1 answer

From a sphere of radius 1m, a sphere of radius 0.5 m is removed from the edge. The shift in the CM is

asked Nov 21, 2013 by meena.p

1 answer

Half of the uniform rectangular plate of length 'L' is made of material of density $d_1$and the other half of density $d_2$. The horizontal distance of center of mass from AB is

asked Nov 21, 2013 by meena.p

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On a large tray of mass M an ice cube of mass m, edge L is kept. If the ice melts completely , the COM of the system comes down by

asked Nov 20, 2013 by meena.p

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Two discs of radius 2 cm and 1 cm, made of the same material are placed as shown . The center of mass from $O_1$ is:

asked Nov 20, 2013 by meena.p

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A uniform disc of radius R is put over another uniform disc of radius 2R of same thickness and density . The peripheries of the two dises touch each other. The position of their COM is

asked Nov 20, 2013 by meena.p

1 answer

Two uniform rods A and B of Lengths 5 m and 3 m are placed end to end. If their linear densities are $3\;kg/m$ and $2\;kg/m$, the position of their centre of mass from their interface is

asked Nov 20, 2013 by meena.p

1 answer

Three identical spheres each of radius 'R' and touching each other so that the centres A,B and C lie on a straight line. The position of their centre of Mass from A is

asked Nov 20, 2013 by meena.p

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The mass of a uniform ladder of Length 5 m is 20 kg. A person of mass 60 kg stands on the ladder at a height of 2 m from the bottom. The position of the center of mass of the ladder and man from the bottom is nearly

asked Nov 20, 2013 by meena.p

1 answer

A uniform wire of length L is bent in the form of a circle. The shift in its centre of mass is

asked Nov 20, 2013 by meena.p

1 answer

Particles of masses $100\;g$ and $300\;g$ have position vectors $(2 \hat {i}+5 \hat {j}+13 \hat {k})$ and $(-6 \hat i +4 \hat j+2 \hat k).$ Position vector of their center of Mass is

asked Nov 20, 2013 by meena.p

1 answer

Center of mass of two particles with masses 2 kg and 1 kg located at (1,0,1) and (2,2,0) has the coordinates of

asked Nov 20, 2013 by meena.p

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The center of mass of a system of particles is at the origin from this we conclude that

asked Nov 20, 2013 by meena.p

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If the external forces acting on a system have zero resultant , the center of mass

asked Nov 20, 2013 by meena.p

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A body has its centre of mass at the origin. The y coordinates of the particles of the body may be 1) all positive 2) all negative 3) all non-zero 4) positive for some cases and negative in other cases. Which of the following is correct ?

asked Nov 20, 2013 by meena.p

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