Question

Two masses - $\sqrt{3}$ m and - $\sqrt{2}$m toed by a light string are placed on a wedge of mass 4 m. The wedge is placed on a smooth horizontal surface. Find out the value of $\theta$ so that the wedge does not move after the system is set free from the state of rest.

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is A

Centre of mass will not shift in horizontal direction.
Let - $\sqrt{3}$ m moves a distance x on wedge in downward direction. - $\sqrt{2}$ m will also move on the other side in downward direction by a distance x .
Then $m_1$$x_1$ = $m_2$$x_2$
$\sqrt{3}$ mx cos${45}^{\circ }$=-$\sqrt{2}$mx cos $\theta$
$\Rightarrow Cos\theta =\frac{\sqrt{3}}{2}\Rightarrow \theta ={30}^{\circ }$