Question

A block of mass m is kept over a fixed smooth wedge. Block is attached to a sphere of same mass through fixed massless pullies $P_1$ and $P_2$. Sphere is dipped inside the water as shown. If specific gravity of material of sphere is $2.$ Find the acceleration of sphere.

Answer 1

$m=2vg$

Tension on string = $mg\sin \theta$

= $\frac{mg}{2}$

& downlward force = $(2-1)vg$

= $vg$

= $mg/2$

Hence the system is in equilibrium i.e. acceleration of sphere is zero.