Question

In the shown figure, the block moves downwards with velocity $V_1$, the wedge moves rightwards with velocity $V_2$. Assuming the surface to be smooth and pulley and string to be ideal, the correct relation between $V_1$ and $V_2$ is

• A. $V_2=V_1$
• B. $V_2=V_1\sin \theta$
• C. $2V_2\sin \theta =V_1$
• D. $V_2(1+\sin \theta )=V_1$

Answer 1

The correct option is D $V_2(1+\sin \theta )=V_1$

The given system can be reframed as shown below

From constrained condition and using intercept method we get
${\stackrel{.}{L}}_1+{\stackrel{.}{L}}_2+{\stackrel{.}{L}}_3=0$
$\Rightarrow V_1-V_2\sin \theta -V_2=0\Rightarrow V_1=V_2+V_2\sin \theta$
$V_1=V_2(1+\sin \theta )$