Work Power and Energy 1 Question 7
8. A uniform chain of length $L$ and mass $M$ is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If $g$ is acceleration due to gravity, the work required to pull the hanging part on to the table is
(1985, 2M)
(a) $M g L$
(b) $M g L / 3$
(c) $M g L / 9$
(d) $M g L / 18$
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Answer:
Correct Answer: 8. (d)
Solution:
- Mass of hanging portion is $M / 3$ (one-third) and centre of mass $c$, is at a distance $h=\frac{L}{6}$ below the table top. Therefore, the required work done is,
$$ W=m g h=\frac{M}{3} \quad(g) \frac{L}{6}=\frac{M g L}{18} $$
