Work Energy and...

A gun is mounted on a trolley free to move on horizontal tracks. Mass of gun and trolley $$25$$ kg. Gun fires a two shells of mass $$5$$ kg each other. Velocity of shells with roll to gun is $$60 $$ m/s . In above question, velocity of gun with respect to ground after firing second shell is-

Two spring of spring constant k and 3k are stretched separately by same force. The ratio of the potential energy stored in them respectively will be 

The P.E of a certain spring a, when stretched from natural through a distance $$0.3m$$, is $$10J$$. The amount of work in joule that must be done on this spring to stretch it through an additional distance $$0.15m$$ will be

A vertical spring of force constant $$100 N/m$$ is attached with a hanging mass of $$10 $$ kg. Now an external force is applied on the mass so that the spring is stretched by the additional $$2$$ m, The work done by the force F is ( $$g= 10 m/s^2$$) 

A ball of mass $$10kg$$ moving with velocity $$20m/s$$ collides elastically with wall and rebound with the same speed.Then the magnitude of change in momentum of the ball will be

$$540$$ calories of heat convert $$1\ cubic\ centimeter$$ of water at $$100^{o}\ C$$ into $$1671\ cubic\ centimeter$$ of steam at $$100^{o}\ C$$ at a pressure of one atmosphere. Then the work done against the atmospheric pressure is nearly:

A bucket full of water weighs $$5$$ kg, it is pulled from a well $$20m$$ deep. There is a small hole In the bucket through which water leaks at a constant rate of $$0.2 k g m ^ { - 1 }.$$ The total work done in pulling the bucket up from the well is $$(g = 10 m s ^ { - 2 } )$$

$$AB$$ is a long frictionless horizontal surface. One end of an ideal spring of spring constant $$K$$ is attached to a block of mass $$m$$ which is being moved left with constant velocity $$v _ { 1 }$$ and another end is free. Another block of mass $$2\mathrm { m }$$ is given a velocity $$3\mathrm { v }$$ towards the spring. The magnitude of work done by the external agent in moving $$m$$ with constant velocity $$v$$ in a long time is $$\beta$$ times $$m v ^ { 2 }$$. Find the value of $$\beta .$$

The average kinetic energy of an idea gas per molecule at $$25^{o}C$$, will be

The mass of object X is $$M_1$$ and that of object Y is $$M_2$$. Keeping their kinetic energy constant, if the velocity of object Y is doubled the velocity of object X, what will be the relation between their masses?