Q 11-06-031NEETJEE MainTop questionMedium
A light string is wound round a pulley (uniform disc) of mass $2$ kg and radius $0.1$ m, free to rotate about a fixed horizontal axis. A $1$ kg block hangs from the free end of the string. The acceleration of the block is ($g = 10\ \text{m/s}^2$)
Answer: (A) $5\ \text{m/s}^2$
Block: $mg - T = ma$. Pulley: $TR = I\alpha = \dfrac{1}{2}MR^2\dfrac{a}{R} \Rightarrow T = \dfrac{Ma}{2}$.
$$a = \frac{mg}{m + M/2} = \frac{10}{1 + 1} = 5\ \text{m/s}^2$$
(The radius cancels.)
Solution by Sreeraj P, M.Sc Physics