Question

A rod of length is sliding such that one of its ends is always in contact with a vertical wall and its other end is always in contact with horizontal surface. Just after the rod is released from rest, the magnitude of acceleration of end points of the rod is $a$ and $b$ respectively. The angular acceleration of rod at this instant will be:

• A. $\frac{a+b}{l}$
• B. $\frac{\sqrt{|a^2-b^2|}}{l}$
• C. $\frac{\sqrt{a^2+b^2}}{l}$
• D. $Noneofthese$

Answer 1

The correct option is C $\frac{\sqrt{a^2+b^2}}{l}$

Acceleration of point A, $\overrightarrow{a_A}=-a$ $\hat{j}$

Acceleration of point B, $\overrightarrow{a_B}=b$ $\hat{i}$

Now, acceleration of point A w.r.t B, $\overrightarrow{a_{AB}}=-a$ $\hat{j}$$-b\hat{i}$

$|\overrightarrow{a_{AB}}|=\sqrt{a^2+b^2}$

$|\overrightarrow{a_{AB}}|=l\alpha ⟹\alpha =\frac{\sqrt{a^2+b^2}}{l}$