Question

Consider the following diagram in which an inextensible string connects two blocks passing via ring. The first block moves with a velocity of $2m{s}^{-1}$ and the second one moves with a velocity of $vm{s}^{-1}$ . If the ring slides on horizontal rod then the value of $v$ is (in $m{s}^{-1}$ )

• A. $\frac{\sqrt{3}}{2}+1$
• B. $\sqrt{\frac{3}{2}}+1$
• C. $\sqrt{\frac{2}{3}+1}$
• D. $\sqrt{\frac{2}{3}}+1$

Answer 1

Answer: (B)

The length of the string will remain constant. Hence,
$2cos30^{\circ }-1cos30^{\circ }=vcos45^{\circ }-1cos45^{\circ }$
$\therefore \frac{v-1}{\sqrt{2}}=\frac{\sqrt{3}}{2}$
$\therefore v=1+\sqrt{\frac{3}{2}}$