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: At the centre of earth, a body has centre of mass, but no centre of gravity**

Statement 2: Acceleration due to gravity is zero at the centre of earth

Statement 2: Acceleration due to gravity is zero at the centre of earth

Solution

(a)

At the centre of earth, g = 0. Therefore a body has no weight at the centre of earth and have no centre of gravity (centre of gravity of a body is the point where the resultant force of attraction or the weight of the body acts). But centre of mass of a body depends on mass and position of particles and is independent of weight

(a)

At the centre of earth, g = 0. Therefore a body has no weight at the centre of earth and have no centre of gravity (centre of gravity of a body is the point where the resultant force of attraction or the weight of the body acts). But centre of mass of a body depends on mass and position of particles and is independent of weight

**Q2. Statement 1: Torque due to force is maximum when angle between r ⃗ and F ⃗ is 90°**

**Statement 2: The unit of torque is newton-metre**

**Q3. Statement 1: The velocity of a body at the bottom of an inclined plane of a given height is more when it slides down the plane compared to when it is rolling down the same plane**

Statement 2: In rolling down, a body acquires both kinetic energy of translation and rotation

Statement 2: In rolling down, a body acquires both kinetic energy of translation and rotation

Solution

(a)

In sliding down, the entire, the potential energy is converted into kinetic energy. Which in rolling, the same part of potential energy is converted into KE of rotation, therefore linear velocity acquired is less

(a)

In sliding down, the entire, the potential energy is converted into kinetic energy. Which in rolling, the same part of potential energy is converted into KE of rotation, therefore linear velocity acquired is less

**Q4. Statement 1: The centre of mass of system of n particles is the weighted average of the position vector of the n particles making up the system**

**Statement 2: The position of the centre of mass of a system is independent of coordinate system**

Solution

NO SOLUTION

NO SOLUTION

**Q5. Statement 1: If no external force acts on a system of particles, then the centre of mass will not move in any direction**

Statement 2: If net external force is zero, then the linear momentum of the system remains constant

Statement 2: If net external force is zero, then the linear momentum of the system remains constant

Solution

(d)

Net external force is zero. Therefore, no acceleration for CM. So, CM may move with a constant velocity

(d)

Net external force is zero. Therefore, no acceleration for CM. So, CM may move with a constant velocity

**Q6. Statement 1: A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity. Then the acceleration of lowest point on the disc is zero**

**Statement 2: For a rigid disc rolling without slipping on a fixed rough horizontal surface, the velocity of the lowest point on the disc is always zero**

Solution

(d)

For a disc rolling without slipping on a horizontal rough surface with uniform angular velocity, the acceleration of the lowest point of disc is directed vertically upward and is not zero(due to translation part of rolling, acceleration of lowest point is zero. Due to rotational part of rolling, the tangential acceleration of the lowest point is zero and centripetal acceleration is non-zero and upwards). Hence, statement I is false. Statement 2 is true

(d)

For a disc rolling without slipping on a horizontal rough surface with uniform angular velocity, the acceleration of the lowest point of disc is directed vertically upward and is not zero(due to translation part of rolling, acceleration of lowest point is zero. Due to rotational part of rolling, the tangential acceleration of the lowest point is zero and centripetal acceleration is non-zero and upwards). Hence, statement I is false. Statement 2 is true

**Q7. Statement 1: Torque is time rate of change of a parameter, called angular momentum**

**Statement 2: This is because in linear motion, force represents time rate of change of linear momentum**

Solution

(d)

Angular momentum is rotational analogue of linear momentum, and torque is rotational analogue of force.

(d)

Angular momentum is rotational analogue of linear momentum, and torque is rotational analogue of force.

**Q8. Statement 1: The position of centre of mass of a body does not depend upon shape and size of the body**

Statement 2: Centre of mass of a body lies always at the centre of the body

Statement 2: Centre of mass of a body lies always at the centre of the body

Solution

(d)

The position of centre of mass of a body depends on shape, size and distribution of mass of the body. The centre of mass does not lie necessarily at the centre of the body

(d)

The position of centre of mass of a body depends on shape, size and distribution of mass of the body. The centre of mass does not lie necessarily at the centre of the body

**Q9. Statement 1: If a sphere of mass m moving with speed u undergoes a perfectly elastic head–on collision with another sphere of heavier mass M at rest ( M > m ) , then direction of velocity of sphere of mass m is reserved due to collision (no external force acts on system of two spheres)**

**Statement 2: During a collision of spheres of unequal masses, the heavier mass exerts more force on the lighter mass in comparison to the force which lighter mass exerts on the heavier one**

Solution

(c)

Statement II contradicts Newton’s third law and hence it is false

(c)

Statement II contradicts Newton’s third law and hence it is false