Question

A bead B of mass ‘m’ can travel without friction on a smooth horizontal wire xx’. The bead is connected to a block of identical mass by an ideal string passing over an ideal pulley. The system, as shown, is in vertical plane.

The system is allowed to fall. Find the speed of block A at the instant when string connected to the bead B makes an angle ${37}^{\circ }$ with vertical.

• A. $\sqrt{ag}$
• B. $\sqrt{\frac{5ag}{17}}$
• C. $\sqrt{\frac{27ag}{68}}$
• D. $\sqrt{\frac{ag}{2}}$

Answer 1

Answer: (B), (C)

The correct options are
B

$\sqrt{\frac{5ag}{17}}$

C

$\sqrt{\frac{27ag}{68}}$

$mg-T=m{a}_1$
$Tcos{30}^{\circ }=m{a}_2$
and $a_{2}cos{30}^{\circ }=a_1$
$\Rightarrow a_1=\frac{3g}{7}$
Height dropped by A
$h=\frac{a}{cos{60}^{\circ }}-\frac{a}{cos{37}^{\circ }}=\frac{3a}{4}$
$mgh=\frac{1}{2}m{v}_A^2+\frac{1}{2}m{v}_B^2$
Also, $v_{B}sin{37}^{\circ }=v_A$
$\Rightarrow \frac{3ag}{4}=\frac{V_A^2}{2}[1+\left(\frac{5}{2}\right)]$
$v_A=\frac{3}{2}\sqrt{\frac{3ag}{17}}$