Question

In the shown figure, block moves downwards with velocity $v_1$, the wedge moves rightwards with velocity $v_2$. 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
${\stackrel{.}{L}}_1+{\stackrel{.}{L}}_2+{\stackrel{.}{L}}_3=0$
$\Rightarrow V_1-V_2\sin \theta -V_2=0\Rightarrow V_1=V_2+V_2\sin \theta$
$V_1=V_2(1+\sin \theta )$