Two particles $A$ and $B$ are released simultaneously from two different inclined planes of inclinat

Question

Two particles $A$ and $B$ are released simultaneously from two different inclined planes of inclination $30^{\circ}$ and $60^{\circ}$, respectively with the horizontal. If $K_A$ and $K_B$ be their kinetic energies when they reach the foot of the inclines after traveling the same distance $L$ along the inclined plane, then the ratio $\frac{K_A}{K_B}$ is

Professor PC Thomas Classes · Answer

$ \begin{aligned} & K_A=m g L \sin 30^{\circ} ; \quad K_B=m g L\sin 60^{\circ} \ & 	herefore \frac{K_A}{K_B}=\frac{\sin 30^{\circ}}{\sin 60^{\circ}}=\frac{1}{\sqrt{3}} \end{aligned} $