Question

Find the ratio of accelerations of rod $A$ and wedge $B$ in the arrangement shown in figure above if the ratio of the mass of the wedge to that of the rod equals $\eta$, and the friction between all contact surfaces is negligible.

• A. $cot\alpha$
• B. $co{t}^2\alpha$
• C. $ta{n}^2\alpha$
• D. $tan\alpha$

Answer 1

The correct option is D $tan\alpha$

Let us draw free body diagram of each body, i.e. of rod $A$ and of wedge $B$ and also draw the kinematical diagram for accelerations, after analysing the directions of motion of $A$ and $B$. Kinematical relationship of accelerations is
$\tan \alpha =\frac{w_A}{w_B}$ (1)