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 mass of a body cannot be considered to be concentrated at the centre of mass of the body for the purpose of computing its moment of inertia**

Statement 2: Then the moment of inertia of every body about an axis passing through its centre of mass would be zero

Statement 2: Then the moment of inertia of every body about an axis passing through its centre of mass would be zero

Solution

(a)

Moment of inertia is the sum of m r

(a)

Moment of inertia is the sum of m r

^{2}terms. We cannot change all the r's, keep m's the same and expect Î£m_{i}r_{i}^{2}to remain unchanged**Q2. Statement 1: The velocity of a body at the bottom of an inclined plane of given height is more when it slides down the plane compared to when it rolls down the same plane**

**Statement 2: In rolling down, a body acquires both, KE of translation and KE of rotation**

Solution

(b)

In sliding down, the entire PE is converted only into linear KE. In rolling down, a part of the same PE is converted into KE of rotation. Therefore, the velocity acquired is less. Both the statements are true, but statement-2 is not a correct explanation of the statement

(b)

In sliding down, the entire PE is converted only into linear KE. In rolling down, a part of the same PE is converted into KE of rotation. Therefore, the velocity acquired is less. Both the statements are true, but statement-2 is not a correct explanation of the statement

**Q3. Statement 1: Many great rivers flow towards the equator. The sediments that they increases the time of rotation of the earth about its own axis**

Statement 2: The angular momentum of the earth about its rotation axis is conserved

Statement 2: The angular momentum of the earth about its rotation axis is conserved

Solution

(a)

Sediment deposited at the equator (away from the axis of rotation) increases the moment of inertia (not mass) of the Earth. Since IÏ‰ = constant, Ï‰ decreases and thus I = 2Ï€/Ï‰ increases

(a)

Sediment deposited at the equator (away from the axis of rotation) increases the moment of inertia (not mass) of the Earth. Since IÏ‰ = constant, Ï‰ decreases and thus I = 2Ï€/Ï‰ increases

Solution

(a)

Position vector of centre of mass depends on masses of particles and their location. Therefore, change in shape/size of body do change the centre of mass

(a)

Position vector of centre of mass depends on masses of particles and their location. Therefore, change in shape/size of body do change the centre of mass

**Q5. Statement 1: If a ball projected up obliquely from the ground breaks up into several fragments in its path, the centre of the system of all fragments moves in the same parabolic path compared to initial one till all fragments are in air**

Statement 2: In the situation of Statement 1, at the instant of breaking, the fragments may be thrown in different directions with different speeds

Statement 2: In the situation of Statement 1, at the instant of breaking, the fragments may be thrown in different directions with different speeds

Solution

(b)

The center of mass of the fragments will continue its parabolic path. After the breakage, fragments may move in different directions. Both statements are correct, but Statement II is not the explanation of Statement I

(b)

The center of mass of the fragments will continue its parabolic path. After the breakage, fragments may move in different directions. Both statements are correct, but Statement II is not the explanation of Statement I

**Q6. Statement 1: Moment of inertia of a particle is same, whatever be the axis of rotation**

Statement 2: Moment of inertia depends on mass and distance of the particles

Statement 2: Moment of inertia depends on mass and distance of the particles

Solution

(a)

The moment of inertia of a particle about an axis of rotation is given by the product of the mass of the particle and the square of the perpendicular distance of the particle from the axis of rotation. For different axis, distance would be different, therefore moment of inertia of a particle changes with the change in axis of rotation

(a)

The moment of inertia of a particle about an axis of rotation is given by the product of the mass of the particle and the square of the perpendicular distance of the particle from the axis of rotation. For different axis, distance would be different, therefore moment of inertia of a particle changes with the change in axis of rotation

**Q7. Statement 1: A body cannot have energy without having momentum but it can have momentum without having energy**

**Statement 2: Momentum and energy have different dimensions**

**Q8. Statement 1: In a two–body collision, the momenta of the particles are equal and opposite to one another, before as well as after the collision when measured in the centre of mass frame**

Statement 2: The momentum of the system is zero from the centre of mass frame

Statement 2: The momentum of the system is zero from the centre of mass frame

**Q9. Statement 1: A ladder is more likely to slip when a person is near the top than when he is near the bottom**

**Statement 2: The friction between the ladder and the floor decreases as he climbs up**

Solution

(c)

As the person climbs up, normal reaction and friction between the ladder and the wall both increases. This decreases normal reaction from the floor, decreasing limiting value of friction there. This increases the possibility of the ladder to ship

(c)

As the person climbs up, normal reaction and friction between the ladder and the wall both increases. This decreases normal reaction from the floor, decreasing limiting value of friction there. This increases the possibility of the ladder to ship

**Q10. Statement 1: A shell at rest, explodes. The centre of mass of fragments moves along a straight path**

**Statement 2: In explosion the linear momentum of the system remains always conserved**

Solution

(a)

As the shell is initially at rest and after explosion, according to law of conservation of linear momentum, the center of mass remains at rest. While parts of shell move in all direction, such that total momentum of all parts is equal to zero

(a)

As the shell is initially at rest and after explosion, according to law of conservation of linear momentum, the center of mass remains at rest. While parts of shell move in all direction, such that total momentum of all parts is equal to zero