Work Energy and...

A force of $$5N$$ acts on a $$15kg$$ body initially at rest. The work done by the force during the first second of motion of the body is:

A chain is held on a frictionless table with $$L/4$$ hanging over. Knowing total mass of the chain is $$M$$ and total length is $$L$$, the minimum work required to pull hanging part back too the table is:

The time period of a simple harmonic pendulum in a stationary train is $$T$$. The time period of a mass attached to a spring is also $$T$$. The train accelerates at the rate $$5 ms^{-2}$$. If the new time periods of the pendulum and spring be $$T_p$$ and $$T_s$$ respectively, then 

A small solid sphere of mass $$m$$ is released from a point $$A$$ at a height $$h$$ above the bottom of a rough track as shown in the figure. If the sphere rolls down the track without slipping, its rotational kinetic energy when it comes to the bottom of track is

Select the incorrect option:-
($$\tau = torque, \,v = velocity, \,\omega = angular \,velocity, \, a_c = centripetal \, acceleration$$)

A worker lifts a $$20.0 kg$$ bucket of concrete from the ground up to the top of a $$20.0 m$$ tall building. What is the amount of work that the worker did in lifting the bucket?

A block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in the figure. Initially, the spring is in the natural state. Then the maximum positive work that the applied force $$F$$ can do is: (Given that spring does not break)

A bob of mass $$m$$ is attached at one end of a string of length $$\iota $$. Other end of the string is fixed point $$O$$. Bob is rotating in circular path of radius $$\iota $$ in horizontal plane about $$O$$ with constant speed $$v$$, as shown in the figure. The average force exerted by string on the bob during its:

The work done in extending a spring by $$x_0$$ is $$W_0$$. Find the work done in further extension $$x_0$$.

A solid sphere of mass $$4kg$$ and radius $$1m$$ is rotating about the given axis $$xx'$$ with angular velocity $$10rad/s$$ shown in figure. The $${K.E}_{rotation}$$ is given by