A small ball B of mass m is suspended with light inelastic string… - Vidyadip

MCQ

$A$ small ball $B$ of mass $m$ is suspended with light inelastic string of length $L$ from $a$ block $A$ of same mass $m$ which can move on smooth horizontal surface as shown in the figure. The ball is displaced by angle $\theta$ from equilibrium position & then released. The displacement of block when ball reaches the equilibrium position is

✓
$\frac{{L\sin \theta }}{2}$
B
$L\,sin\theta$
C
$L$
D
none of these

✓

Answer

Correct option: A.

$\frac{{L\sin \theta }}{2}$

a
If ball and blocks are taken as system, then in horizontal direction no external force is present. Hence, centre of mass remains in rest in horizontal direction.

$m(L \sin \theta-x)-m_{x}=0$

Or $\mathrm{mL} \sin \theta-\mathrm{mx}-\mathrm{mx}=0$

$\mathrm{x}=\frac{\mathrm{L}}{2} \sin \theta$

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