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.

System is initially released from rest in the position shown. Initial acceleration of block A is:

• A. zero
• B.
  $\frac{g}{2}$
• C. $\frac{3g}{7}$
• D. $\frac{4g}{7}$

Answer 1

Answer: (B), (C)

The correct options are
B

$\frac{g}{2}$

C

$\frac{3g}{7}$

$mg-T=m{a}_1$
$Tcos{30}^{\circ }=m{a}_2$
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, $v_{B}sin{37}^{\circ }=v_A$
$\Rightarrow \frac{3ag}{4}=\frac{V_A^2}{2}[1+\left(\frac{5}{2}\right)]$
$v_A=\frac{3}{2}\sqrt{\frac{3ag}{17}}$