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For a circular ring, centre of gravity lies,

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Important Questions on Laws of Motion

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A hollow metallic bob is filled with a liquid. A small hole is drilled just below the centre of gravity of the bob so that the liquid slowly drops out of it. Water drops out continuously and the bob gets empty of liquid. In this entire process centre of gravity
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In the given experiment find the value of unknown mass m.

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Centre of mass is a point
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Assertion: The centre of mass of a body may lie where there is no mass.
Reason: Centre of mass of a body is a point, where the whole mass of the body is supposed to be concentrated.
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Find the distance between centre of gravity and centre of mass of a two particle system attached to the ends of a light rod. Each particle has the same mass. Length of the rod is R, where R is the radius of the Earth.

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Which of the following statements are correct ? 

A Centre of mass of a body always coincides with the centre of gravity of the body
B Centre of mass of a body is the point at which the total gravitational torque on the body is zero
C A couple on a body produce both translational and rotation motion in a body
D Mechanical advantage greater than one means that small effort can be used to lift a large load
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A system consists of 3 particles each of mass m, located at 1,1 2,2 and 3,3 respectively. The co-ordinates of the centre of mass of system are
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Two bodies A and B are attracted towards each other (beginning at rest) due to gravitation. Given that A is much heavier than B, which of the following correctly describes the motion of the centre of mass of the bodies?