Work power energy is the most important chapter when it comes to mechanics, for JEE (Advanced). The chapter is quite tricky and takes a lot of time and devotion on your part to understand and master. But this chapter is a complete gold medal for almost all the questions of the mechanics can be solved by the work power energy approach if you master this topic..

**Q1.**

**Statement 1:**The change in kinetic energy of a particle is equal to the work done on it by the net force

**Statement 2:**Change in kinetic energy of particle is equal to the work done only in case of a system of one particle

Solution

Change in kinetic energy = work done by net force
This relationship is valid for particle as well as system of particles

**Q2.**

**Statement 1**:The kinetic energy of a system can be increased without applying any external force on the system

**Statement 2:**Single external force acting on a particle necessarily changes its kinetic energy

Solution

Work done by internal force=change in kinetic energy
If F ext=0,F(n.C)=0
During motion of circular path work done by the centripetal force is zero

**Q3.**

**Statement 1:**Mass and energy are not conserved separately, but are conserved as a single entity called mass-energy J

**Statement 2**: Mass and energy conservation can be obtained by Einstein equation for energy

Solution

From Einstein equation E=mc^2

**Q4.**

**Statement 1:**A car and a heavy lorry moving on a road have same speed. Same braking force is applied and both stop in same distance

**Statement 2:**Same fore will cause different retardation in two vehicles

Solution

Since mass of carmass of lorry. Retardation on car is more than lorry. And car will stop earlier; at lesser distance

**Q5.**

**Statement 1:**When a gas is allowed to expand, work done by gas is positive

**Statement 2:**Force due to gaseous pressure and displacement (of piston) are in the same direction

Solution

Since the gaseous pressure and the displacement (of piston) are in the same direction. Therefore Î¸=0°
∴ Work done =Fs cosÎ¸=Fs= Positive
Thus during expansion work done by gas is positive

**Q6.**

**Statement 1:**The work done by a conservative force during a round trip is always zero

**Statement 2:**No force is required to move a body in its round trip

Solution

During a round trip, the body finally comes at its initial position, i.e., the displacement of body is equal to zero. Therefore, work done is equal to zero. So W=F ⃗.S ⃗=0. Statement I is correct and statement II is wrong

**Q7.**

**Statement 1:**A heavy weight is suspended from a string. A person raises the weight slowly till the spring becomes slack. The work done by the person inW. The energy stored on the

**Statement 2:**The work done by the spring force is always negative

Solution

W(mg)+W(spring)+W(Man)=0-∆U+E+W=0
∆U=E+W
Work done by spring force is positive when a compressed spring is released or stretched spring is released

**Q8.**

**Statement 1:**A quick collision between two bodies is more violent than slow collision, even when initial and final velocities are identical

**Statement 2:**The rate of change of momentum determines that force is small or large

Solution

In a quick collision, time t is small. As F×t= constant, therefore, force involved is large, i.e. collision is more violent in comparison to slow collision

Solution

The maximum extension is non-zero, whole the spring never undergoes compression. Hence, statement I is false

**Q10.**

**Statement 1:**In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision

**Statement 2:**In an elastic collision, the linear momentum of the system is conserved

Solution

Both the statement 1 & statement 2 is true, statement 2 is not a correct explanation for statement 1. In fact the momentum is conserved both in elastic as well as in inelastic collision. But in elastic collision the total kinetic energy of the system is also conserved