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 $g=10\,ms^{-2}$]

For the system shown in the figure,if $M_1 = 10 \ kg$,$M_2 = 5 \ kg$,$\theta = 30^\circ$,and $g = 10 \ m/s^2$,find the tension in the string in $N$.

As shown in the figure,an iron block $A$ of volume $0.25 \ m^3$ is attached to a spring $S$ of unstretched length $1.0 \ m$ and hanging from the ceiling. The spring gets stretched by $0.2 \ m$. This block is removed and another iron block $B$ of volume $0.75 \ m^3$ is now attached to the same spring and kept on a frictionless inclined plane of $30^{\circ}$ inclination. The distance of the block from the top along the incline at equilibrium is (in $m$)

An object requires $500 \,N$ force to be pulled up on a $30^{\circ}$ frictionless smooth inclined plane at a constant speed. The weight of the object is

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?

$A$ double inclined plane as shown in the figure has a fixed horizontal base and smooth faces with the same angle of inclination of $30^{\circ}$. $A$ block of mass $m_2 = 300 \ g$ is on one face and is connected by a cord passing over a frictionless pulley to a second block of mass $m_1 = 200 \ g$ kept on the other face. The acceleration with which the system of the blocks moves is ........ $\%$ of acceleration due to gravity $(g)$.