Laws of Motion ...

A railway track is banked for a speed v, by making the height of the outer rail h higher than that of the inner rail. The distance between the rails is d. The radius of curvature of the track is r. Then, 

Two identical balls $$A$$ and $$B$$ are connected with massless rod $$AB$$ and moves in a smooth circular track of radius $$R. OB$$ is horizontal and $$PQ = R\left (1 - \dfrac {\sqrt {3}}{2}\right )$$. Find the equation by which maximum value of $$\theta$$ can be obtained, where $$\theta$$ is the angle that new position of ball $$B$$ makes at $$O$$ with horizontal.

"To every action, there is equal and opposite reaction". It is Newton's

A simple pendulum of length $$L$$ carries a bob of mass $$m$$. When the bob is at its lowest position, it is given the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal the net force on the bob is:

A ball of mass m strikes a rigid wall with speed u and rebounds with the same speed. The impulse imparted to the ball by the wall is:

A car is moving on a frictionless (in the radial direction) circular banked road, with a banking angle of $$15^o$$, find the velocity of the car.
Mass of car is $$600\ kg$$, the radius of the circular road $$=10m$$ 

A bullet of mass 40 g moving with a speed of $$90 ms^{-1}$$ enters a heavy wooden block and is stopped after a distance of 60 cm. The average resistance force exerted by the block on the bullet is

If a car is moving at a velocity $$v$$ in a circular road with coefficient of friction $$\mu$$ and banking angle $$\theta$$. Find the radius of the road such that friction force doesn't act on the car in the radial direction.

The velocity of a body moving in a vertical circle of radius r is $$\sqrt{7gr}$$ at the lowest point of the circle. What is the ratio of maximum and minimum tension?