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 gravity of a body is the point about which the total gravitational torque on the body is zero. (c) A couple on a body produces 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.
(a) and (b)
(b) and (c)
(c) and (d)
(b) and (d)
Statement (a) is incorrect because the centre of mass coincides with the centre of gravity only in a uniform gravitational field. If the gravitational field varies across the body, they may not coincide . Statement (b) is correct. The centre of gravity is defined as the point about which the total gravitational torque on the body is zero . Statement (c) is incorrect. A couple consists of two equal and opposite forces whose lines of action do not coincide. The net force is zero, so it produces pure rotational motion without any translational motion . Statement (d) is correct. Mechanical Advantage (M.A.) is defined as the ratio of load to effort (M.A. = Load / Effort). If M.A. > 1, then Effort < Load, meaning a small effort can lift a large load . Thus, statements (b) and (d) are correct.
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