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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 rotational 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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(b) and (d)

(a) and (b)

(b) and (c)

answer is B.

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Detailed Solution

Mechanical advantage = load / Effort > 1 ⇒ Load > Effort.

For the sake of simplicity , let us take a two particle system. If c be the COM of the system,

$r_{c} = \frac{m_{1} r_{1} + m_{2} r_{2}}{m_{1} + m_{2}}$

Net moment of gravitational force $m_{1}$ g and $m_{2}$ g about C = $m_{1} g (r_{c} - r_{1}) - m_{2} g (r_{2} - r_{c})$

= $(m_{1} + m_{2}) g . r_{c} - (m_{1} r_{1} + m_{2} r_{2}) g = 0$

Hence statements - (b) and (d) are correct.

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