## SYSTEM OF PARTICLES AND ROTATIONAL MOTION QUIZ - 31

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 1 is True, Statement 2 is True; Statement 2 is the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution
(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
•  Statement 1 is True, Statement 2 is True; Statement 2 is the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
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

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 1 is True, Statement 2 is True; Statement 2 is the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
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

Q4.
•  Statement 1 is True, Statement 2 is True; Statement 2 is the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution
(d)
If F > mg sin⁡Î¸, then friction on disc will be in downward direction and if F < mg sin⁡Î¸, then friction on disc will be in upward direction. If F = mg sin⁡Î¸, 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 1 is True, Statement 2 is True; Statement 2 is the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution

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 1 is True, Statement 2 is True; Statement 2 is the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1
• Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
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

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
•  Statement 1 is True, Statement 2 is True; Statement 2 is the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution

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 1 is True, Statement 2 is True; Statement 2 is the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution

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
•  Statement 1 is True, Statement 2 is True; Statement 2 is the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
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

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
•  Statement 1 is True, Statement 2 is True; Statement 2 is the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
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

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