Two bodies of masses $m_{1}=5\,kg$ and $m_{2}=3\,kg$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass $m_{1}$ will be $....N$ [Take $g=10\,ms^{-2}$]

If $M_1 = M_2$ and $\theta = 30^o$,then the acceleration is ........... $ms^{-2}$.

Consider the shown arrangement. Assume all surfaces to be smooth. If $N$ represents the magnitude of the normal reaction between the block of mass $m$ and the wedge of mass $M$,then the acceleration of $M$ along the horizontal equals:

$A$ frictionless wire $AB$ is fixed on a sphere of radius $R$. $A$ very small spherical ball slips on this wire. The time taken by this ball to slip from $A$ to $B$ is

Given $M_1 = 10 \ kg$,$M_2 = 5 \ kg$,$\theta = 30^o$,and $g = 10 \ m/s^2$. What is the acceleration of the system?

Two inclined frictionless tracks,one gradual and the other steep,meet at $A$ from where two stones are allowed to slide down from rest,one on each track. Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given $\theta_{1}=30^{\circ}, \theta_{2}=60^{\circ},$ and $h=10 \; m,$ what are the speeds and times taken by the two stones?