Rotation 3 Question 1
7. A mass $m$ supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, with what acceleration will the mass fall on release? (2014 Main)
(a) $2 g / 3$
(b) $g / 2$
(c) $5 g / 6$
(d) $g$
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Answer:
Correct Answer: 7. (b)
Solution:
- For the mass $m, m g-T=m a$
As we know, $\quad a=R \alpha$
So, $\quad m g-T=m R \alpha$
Torque about centre of pully
$$ T \times R=m R^{2} \alpha $$
From Eqs. (i) and (ii), we get, $a=g / 2$
Hence, the acceleration with the mass of a body fall is $g / 2$.
