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Question

Which of the following statements are correct?
1. Centre of mass of a body always coincides wiith the centre of gravity of the body.
2. Centre of gravity of a body is the point where total gravitational torque on the body is zero.
3. A couple on a body produces both translational and rotational motion in a body.
4. Mechanical advantage greater than one means that a small effort can be used to lift a large load.

A
(1) and (2)
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B
(2) and (3)
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C
(3) and (4)
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D
(2) and (4)
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Solution

The correct option is D (2) and (4)

Force due to gravity always acts at centre of gravity, hence the torque of gravitational force about centre of gravity will be zero, since mg will pass through this point and τmg=0

Mechanical advantage=Output forceInput force
M.A>1 Foutput>Finput
hence larger load can be lifted by applying smaller force.

In a couple two equal and opposite forces acts, hence Fnet=0 but τnet0 for a couple. So, rotational motion is produced in case of couple.


Centre of mass and centre of gravity coincides only in case of symmetrical objects.
Option (d) is correct.

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