Question

The two blocks are moving with constant velocities as shown in the diagram. Assume that the surface is smooth and string is inextensible.
Mark the correct option(s)

• A. The value of $V_0$ is $4{\text{m/s}}^2$
• B. The value of $V_0$ is $5{\text{m/s}}^2$
• C. The value of $\theta$ is $37°$
• D. The value of $\theta$ is $53°$

Answer 1

Answer: (B), (D)

The correct options are
B The value of $V_0$ is $5{\text{m/s}}^2$
D The value of $\theta$ is $53°$

Let the x-component of velocity of pulley be $V_x$ and y-component of velocity be $V_y$

Equating components of velocity along the length for both blocks

$V_x\cos \theta +V_y\sin \theta =4-V_x\cos 30°+V_y\sin 30°=2.5$
If $V_x=0\Rightarrow V_0=V_y=\frac{4}{\sin \theta }=\frac{2.5}{\sin 30°}$
$\therefore V_0=5;\theta =53°$