JEE Advanced paper is considered to be one of the toughest entrance exams in India. Moreover, this Physics is considered the toughest subject because it is the most application-based. The student needs to get the basics right and then move on to mastering advanced concepts. System of Particles and Rotational motion consists of nearly about 6-7 % of marks in the Physics section.

**Q1. Statement 1: The centre of mass of a two particle system lies on the line joining the two particles, being closer to the heavier particle**

Statement 2: This is because product of mass of one particle and its distance from centre of mass in numerically equal to product of mass of other particle and its distance from centre of mass

Statement 2: This is because product of mass of one particle and its distance from centre of mass in numerically equal to product of mass of other particle and its distance from centre of mass

Solution

(a)

The assertion is true, and reason is correct explanation of the assertion.

(a)

The assertion is true, and reason is correct explanation of the assertion.

**Q2. Statement 1: The centre of mass of a body may lie where there is no mass**

**Statement 2: Centre of mass of a body is a point, where the whole mass of the body is supposed to be concentrated**

Solution

(a)

As the concept of centre of mass is only theoretical, therefore in practice no mass may lie at the centre of mass. For example, centre of mass of a uniform circular ring is at the centre of the ring where there is no mass

(a)

As the concept of centre of mass is only theoretical, therefore in practice no mass may lie at the centre of mass. For example, centre of mass of a uniform circular ring is at the centre of the ring where there is no mass

**Q3. Statement 1: A block is kept at the top of a smooth wedge which is kept on a smooth horizontal surface. As the block slides down the wedge, centre of the mass of the system will be accelerated**

Statement 2: When external force acting on the system is zero, centre of mass is in rest

Statement 2: When external force acting on the system is zero, centre of mass is in rest

Solution

(c)

Net force acting on the wedge and block system is gravity; therefore it is accelerated in downward direction. If external force acting on the system is zero, CM may be in rest or moving with constant velocity

(c)

Net force acting on the wedge and block system is gravity; therefore it is accelerated in downward direction. If external force acting on the system is zero, CM may be in rest or moving with constant velocity

Solution

(d)

If F > mg sinÎ¸, then friction on disc will be in downward direction and if F < mg sinÎ¸, then friction on disc will be in upward direction. If F = mg sinÎ¸, then no friction will act on disc. Hence, statement I is false

Statement II is true because in pure rolling, friction can be either static or no friction

(d)

If F > mg sinÎ¸, then friction on disc will be in downward direction and if F < mg sinÎ¸, then friction on disc will be in upward direction. If F = mg sinÎ¸, then no friction will act on disc. Hence, statement I is false

Statement II is true because in pure rolling, friction can be either static or no friction

**Q5. Statement 1: When a diver dives, the rotational kinetic energy of the diver increases during several somersaults**

Statement 2: When diver pulls his limbs, the moment of inertia decreases and on account of conservation of angular momentum his angular speed increases

Statement 2: When diver pulls his limbs, the moment of inertia decreases and on account of conservation of angular momentum his angular speed increases

**Q6. Statement 1: A particle strikes head-on with another stationary particle such that the first particle comes to rest after collision. The collision should necessarily be elastic**

Statement 2: In elastic collision, there is no loss of momentum of the system of the particles

Statement 2: In elastic collision, there is no loss of momentum of the system of the particles

Solution

(d)

If the collision is elastic, then masses of both particles should be same. But if masses are different, then collision is inelastic. Further, momentum remains conserved in any kind of collision

(d)

If the collision is elastic, then masses of both particles should be same. But if masses are different, then collision is inelastic. Further, momentum remains conserved in any kind of collision

**Q7. Statement 1: Torque is equal to rate of change of angular momentum**

**Statement 2: Angular momentum depends on moment of inertia and angular velocity**

**Q8. Statement 1: If there is no external torque on a body about is center of mass, then the velocity of the center of mass remains constant.**

Statement 2: The liner momentum of an isolated system remains constant.

Statement 2: The liner momentum of an isolated system remains constant.

**Q9. Statement 1: The centre of mass of a proton and an electron, released from their respective positions remains at rest**

**Statement 2: The centre of mass remain at rest, if no external force is applied**

Solution

(a)

Initially the electron and proton were at rest so their centre of mass will be at rest. When they move towards each other under mutual attraction then velocity of centre of mass remains unaffected because external force on the system is zero

(a)

Initially the electron and proton were at rest so their centre of mass will be at rest. When they move towards each other under mutual attraction then velocity of centre of mass remains unaffected because external force on the system is zero

**Q10. Statement 1: No external force acts on a system of two spheres which undergo a perfectly elastic head–on collision. The minimum kinetic energy of this system is zero if the net momentum of the system is zero**

**Statement 2: If any two bodies undergo a perfectly elastic head–on collision, at the instant of maximum deformation, the complete kinetic energy of the system is converted to deformation potential energy of the system**

Solution

(c)

For a system of two isolated spheres having non–zero initial kinetic energy, the complete kinetic energy can be converted to other forms of energy if the momentum of the system is zero. This is due to the fact that for an isolated system, the net momentum remains conserved. If an isolated system has non–zero momentum, for the momentum to remain constant, complete kinetic energy of the system cannot become zero. Hence, Statement I is true while Statement II is false

(c)

For a system of two isolated spheres having non–zero initial kinetic energy, the complete kinetic energy can be converted to other forms of energy if the momentum of the system is zero. This is due to the fact that for an isolated system, the net momentum remains conserved. If an isolated system has non–zero momentum, for the momentum to remain constant, complete kinetic energy of the system cannot become zero. Hence, Statement I is true while Statement II is false