Work Energy and...

A particle moves under the effect of a force $$F = C x$$ from $$x = 0$$ to $$ x = x_{1}$$. The work done in the process is (treat $$C$$ as a constant):

 A body of mass 5 kg moving with a speed of $$ 3 ms^{-1}$$ collides head on with a body of mass 3 kg moving in the opposite direction at a speed of $$2 ms^{-1}$$. The first body stops after the collision. Find the final velocity of the second body.

 A heavy steel ball of mass greater than 1 kg moving with a speed of 2m/ s collides head on with a stationary ping pong ball of mass less than 0.1 g. The collision is elastic. After the collision the ping pong ball moves approximately with a speed

A ball of mass M moving with a velocity V collides head on elastically with another of same mass but moving with a velocity v in the opposite direction. After collision,

 A heavier body moving with certain velocity collides head on elastically with a lighter body at rest. Then

A rain drop of mass (1/10) gram falls vertically at constant speed under the influence of the forces of gravity and viscous drag. In falling through 100 m, the work done by gravity is

A body of mass m is rotated at uniform speed along a vertical circle with the help of light string. If $$T_{1} and \ T_{2}$$ are tensions in the string when the body is crossing highest and lowest point of the vertical circle respectively, then which of the following expressions is correct?

 A ball moving with a speed of 2.2 m/sec strikes an identical stationary ball. After collision the first ball moves at 1.1 m/sec at $$60^{0}$$  with the original line of motion. The magnitude and direction of the ball after collision is 

A 50 gm ball collides with another ball of mass 150gm, moving in its direction of motion, After collision the two balls move at a an angle $$30^{0}$$ with their initial direction. Ratio of their velocities after collision is

A body is moving in a vertical circle such that the velocities of body at different points are critical. The ratio of velocities of body at angular displacements $$60^{0}$$ and $$120^{0}$$ from the lowest point is: