Question

A ball connected with string is released at an angle ${45}^{\circ }$ with the vertical as shown in the figure. Then the acceleration of the box at this instant will be
[Mass of the box is equal to the mass of ball].

• A. $g/4$
• B. $g/3$
• C. $g/2$
• D. None of these

Answer 1

The correct option is C $g/2$

$T\cos \theta =mg$

$T=\frac{mg}{\cos \theta }$

$T\sin \theta =ma$

$a=\frac{T\sin \theta }{m}=g\tan \theta$ where $\theta =45°$

$a=g$

Now accelaration of center of mass is all zero.

$\frac{ma-(m+m)a_1}{m+(m+m)}=0$

$a_1=\frac{g}{2}$