A cord is wrapped on a pulley (disc) of mass M and radius R as shown in the figure. To one end of the cord, a block of mass M is connected as shown and to other end
in (a) a force of 2 Mg and in (b) a block of mass 2M. Let angular acceleration of the disc in (a) and (b) is $α_{A}$ and $α_{B}$ , respectively, then (cord is not slipping on the pulley).

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

$α_{A} < α_{B}$

none of these

$α_{A} > α_{B}$

$α_{A} = α_{B}$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$\begin{array}{l} In the figure, (T_{2} - T_{1}) R = \frac{M R^{2}}{2} α_{A} \\ \begin{aligned} T_{1} - M g = M a_{A} \\ T_{2} = 2 M g \\ a_{A} = R α_{A} \\ α_{A} = \frac{2 g}{3 R} \end{aligned} \end{array}$

From the figure,

$\begin{array}{l} (T_{2} - T_{1}) \times R = \frac{M R^{2}}{2} α_{B} \\ T_{1} - M g = M a_{B} \\ 2 M g - T_{2} = 2 M a_{B} \\ a_{B} = R α_{B} \\ α_{B} = \frac{2 g}{7 R} \\ So, α_{A} > α_{B} \end{array}$