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:**Comets move around the sun in elliptical orbits. The gravitational force on the comet due to sun is not normal to the comet’s velocity but the work done by the gravitational force over every complete orbit of the comet is zero

**Statement 2:**Gravitational force is a non conservative force

Solution

The gravitational force on the comet due to the sun is a conservative force. Since the work done by a conservative force over a closed path is always zero (irrespective of the nature of path), the work done by the gravitational forces over every complete orbit of the comet is zero

**Q2.**

**Statement 1:**Work done in moving a body over a closed loop is zero for every force in nature

**Statement 2**: Work done does not depend on nature of force

Solution

Work done in the motion of a body over a closed loop is zero only when the body is moving under the action of conservative forces (like gravitational or electrostatic forces). i.e. work done depends upon the nature of force

**Q3.**

**Statement 1:**In a circular motion, work done by centripetal force is not zero always

**Statement 2:**If the speed of a particle increases or decreases in circular motion, net force acting on the particle does not remain towards centre

Solution

Centripetal force is always perpendicular to velocity, hence it does no work
If speed of the body changes, then additional tangential force comes into play and resultant force does not remain towards centre

**Q4.**

**Statement 1**: According to law of conservation of mechanical energy change in potential energy is equal and opposite to the change in kinetic energy.

**Statement 2:**Mechanical energy is not conserved.

Solution

According to conservation of mechanical energy as for conservation forces the sum of kinetic energy and potential energy remains constant and throughout the motion it is independent of time. This is the law of conservation of mechanical energy.
ie, KE+PE=total energy =constant.

**Q5.**

**Statement 1:**When two moving bodies collide, their temperatures rise.

**Statement 2:**The potential energy of the colliding bodies converts into heat energy.

Solution

When two moving bodies collide, their temperatures rise due to some part of KE is converted into heat energy of two colliding bodies.

**Q7.**

**Statement 1:**Kinetic energy of a body is quadrupled, when its velocity is doubled

**Statement 2:**Kinetic energy is proportional to square of velocity

Solution

K=1/2 mv^2∴K∝v^2
If velocity is doubled then K.E. will be quadrupled

**Q8.**

**Statement 1**: A spring has potential energy, Whether it is compressed or stretched.

**Statement 2**: In compressing or stretching work is done on the spring against the restoring force.

Solution

When a spring is compressed or stretched, work is to be done against restoring force. This work done is stored in the spring in from of potential energy

**Q9.**

**Statement 1**: The internal potential energy of a certain amount of liquid when spread out in a thin layer is more than that of the same amount of liquid in the shape of a sphere

**Statement 2:**The potential energy decreases on account of decreased intermolecular distance

Solution

The potential energy of two identical molecules increases when the distance between them is increased

**Q10.**Statement 1: Mass and energy are not conserved separately, but are conserved as a single identity called mass energy. Statement 2: This is because one can be obtained at the cost of the other as per Einstein equation, E=mc2.

Solution

Einstein mass-energy equivalence relation is given by
E=mc^2
From the relation, it can be said that if energy is conserved, then mass is conserved or vice-versa. Also, per this equation, Whole of the energy can be converted into mass or can be converted wholly into energy.