Work Energy and...

A particle of mass m has a velocity $$-v_{0}\hat{i}$$. while a second particle of same mass has a velocity $$v_{0}j$$. After the particles collide, first particle is found to have a velocity $$\dfrac{-1}{2}v_{0}\hat{i}$$ then the velocity of other particle is

 A wagon of mass 10 tons moving at a speed of 12 kmph collides with another wagon of mass 8 tons moving on the same track in the same direction at a speed of 10 kmph. If the speed of the first wagon decreases to 8 kmph. Find the speed of the other after collision

A ball of mass 0.6kg attached to a light inextensible string rotates in a vertical circle of radius 0.75m such that it has speed of 5 m/s when the string is horizontal. Tension in string when it is horizontal on other side is:

A simple pendulum is oscillating with an angular amplitude $$60^{0}$$ . If mass of bob is $$50\ g$$, the tension in the string at mean position is:

 A 6 kg mass travelling at $$2.5$$ ms$$^{-1}$$ collides head on with a stationary 4 kg mass. After the collision the 6 kg mass travels in its original direction with a speed of $$1$$ ms$$^{-1}$$. The final velocity of 4 kg mass

A pilot of mass $$m$$ can bear a maximum apparent weight $$7$$ times of $$mg$$. The aeroplane is moving in a vertical circle. If the velocity of aeroplane is $$210\ m/s$$ while driving up from the lowest point of vertical circle, the minimum radius of vertical circle should be:

A body of mass $$2\ kg$$ attached at one end of light string is rotated along a vertical circle of radius $$2\ m$$. If the string can withstand a maximum tension of $$140.6\ N$$, the maximum speed with which the stone can be rotated is:

A body is revolving in a vertical circle of radius r such that the sum of its $$K.E.$$ and $$P.E.$$ is constant. If the speed of the body at the highest point is $$\sqrt{2gr}$$ then the speed of the body at the lowest point will be:

A simple pendulum is oscillating with an angular amplitude $$60^o$$. If $$m$$ is mass of bob and $$T_1$$, $$T_2$$ are tensions in the string, when the bob is at extreme position, mean position respectively then is:

The bob of a simple pendulum at rest position is given a velocity $$V$$ in horizontal direction so that the bob describes vertical circle of radius equal to length of pendulum $$l$$ . If the tension in string is $$4$$ times weight of bob when the string is horizontal, the velocity of bob when it is crossing highest point of vertical circle is: