Question

A rod of mass M and length $\sqrt{2}R$ is released from rest inside smooth fixed sphere of radius R.

• A. Acceleration of end A and end B of rod are same
• B. Angular acceleration of rod is $\frac{3g}{4R}$
• C. Acceleration of end A is $\frac{37}{4}m/s^2$
• D. Angular acceleration of rod is $\frac{2g}{3R}$

Answer 1

Answer: (A), (B)

The correct options are
A Acceleration of end A and end B of rod are same
B Angular acceleration of rod is $\frac{3g}{4R}$


$T_0=mg\frac{R}{2}$, $T_0=I_0\alpha$

$I_0=\frac{M(\sqrt{2}R{)}^2}{12}+M{\left(\frac{R}{\sqrt{2}}\right)}^2=M{R}^2[\frac{1}{6}+\frac{1}{2}]$

$Mg\frac{R}{2}=\frac{2}{3}M{R}^2\alpha \Rightarrow \alpha =\frac{3g}{4R}$

$a_A=a_B=R\alpha$