Question

A uniform rod of mass 2kg and length 5m is attached to smooth hinge at end A and to a string at end B as shown in figure. It is at rest. The horizontal acceleration of centre of mass of the rod, just after the string is cut is :

• A. $\frac{3\sqrt{3}g}{4}m/s^2$
• B. $\frac{3g}{16}m/s^2$
• C. Zero
• D. $\frac{3\sqrt{3}g}{16}m/s^2$

Answer 1

The correct option is D $\frac{3\sqrt{3}g}{16}m/s^2$

At the instant string is cut :
$mg.\frac{l}{4}=\frac{m{l}^2}{3}.\alpha \Rightarrow \alpha =\frac{3g}{4l}$
$a_{cm}=\alpha \frac{l}{2}=\frac{3g}{8}$
$\Rightarrow {\alpha }_{horizontal}=a_{cm}sin\theta =\frac{3g}{8}\times \frac{\sqrt{3}}{2}=\frac{3\sqrt{3}g}{16}m/s^2$