Question

An L shaped rod of mass m and dimensions as shown in figure is hinged at one end and is tied to string at the other end. As soon as we cut string,

• A. Angular acceleration of rod is $\frac{3g}{10L}$
• B. Acceleration of point C is $\frac{3g\sqrt{2}}{10}m/s^2$
• C. Acceleration of point C is $\frac{3g}{10}m/s^2$
• D. Acceleration of point B is $\frac{3g}{10}m/s^2$

Answer 1

Answer: (A), (B), (D)

The correct options are
A Angular acceleration of rod is $\frac{3g}{10L}$
B Acceleration of point C is $\frac{3g\sqrt{2}}{10}m/s^2$
D Acceleration of point B is $\frac{3g}{10}m/s^2$


${\tau }_A=\frac{m}{2}g\frac{L}{2}=\frac{mgL}{4}$

$I_A=\frac{M}{2}\frac{L^2}{3}+[\frac{M}{2}\frac{L^2}{12}+\frac{m}{2}\times \frac{5L^2}{4}]$

$I_A=\frac{5}{6}m{L}^2$

${\tau }_A=I_A\alpha \Rightarrow \frac{mgL}{4}=\frac{5}{6}m{L}^2\alpha \Rightarrow \alpha =\frac{3g}{10L}$

$a_C=\sqrt{2}L\alpha =\frac{3\sqrt{2}g}{10}$

$a_B=L\alpha =\frac{3g}{10}$