Question

Consider the following diagram in which an inextensible string connects two blocks passing via ring. The first block moves with a velocity of $2 \, m \, s^{- 1}$ and the second one moves with a velocity of $v \, m \, s^{- 1}$ . 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 $
$\therefore \, \, \frac{v - 1}{\sqrt{2}}=\frac{\sqrt{3}}{2}$
$\therefore \, \, v=1+\sqrt{\frac{3}{2}}$