## SYSTEM OF PARTICLES AND ROTATIONAL MOTION QUIZ - 32

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 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

Q2. Statement 1: Moment of inertia of circular ring about a given axis is more than moment of inertia of the circular disc of same mass and same size, about the same axis
Statement 2: The circular ring hollow so its moment of inertia is more than circular disc which is solid
•  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
(b)
In the case of circular ring the mass is concentrated on the rim (at maximum distance from the axis) therefore moment of inertia increases as compared to that in circular disc

Q3. Statement 1: A ladder is more apt to slip, when you are high up on it than when you just begin to climb
Statement 2: At the high up on a ladder, the torque is large and on climbing up the torque is small
•  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)
When a person is high up on the ladder, then a large torque is produced due to his weight about the point of contact between the ladder and the floor. Whereas when he starts climbing up. The torque is small. Due to this reason, the ladder is more apt to slip, when one is high up on it

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
(a)
Both, the assertion and reason are true, and latter is a correct explanation of the former. In fact, as ice on polar caps of earth melts, mass near the polar axis spreads out, I increases. Therefore, T increases ie, duration of day increases

Q5. Statement 1: The angular momentum under a central force is constant.
Statement 2: Inverse square law of force is conservative.
•  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
(b)
The angular momentum under a central force is a constant and inverse square law of force is conservative.

Q6.
•  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)
The normal force will act non-uniformly to balance the torque of the applied force. Hence, statement I is true. The applied horizontal force F has tendency to rotate the cube in an anticlockwise sense about the centre of the cube. Hence, Statement 2 is false

Q7. Statement 1: The centre of mass of a body may lie where there is no mass
Statement 2: The centre of mass has nothing to do with the 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
(b)
The assertion and reason, both are true. But the reason is not a correct explanation of the assertion. Infact, the centre of mass is related to the distribution of mass of the body

Q8. Statement 1: Inertia and moment of inertia are same quantities
Statement 2: Inertia represents the capacity of a body to oppose its state of motion or 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
(d)
There is a difference between inertia and moment of inertia of a body. The inertia of a body depends only upon the mass of the body but the moment of inertia of a body about an axis not only depends upon the mass of the body but also upon the distribution of mass about the axis of rotation

Q9. Statement 1: The centre of mass of body may lie 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.

Q10. Statement 1: The centre of mass of an electron and proton, when released moves faster towards proton
Statement 2: This is because proton is heavier
•  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)
The position of centre of mass of electron and proton remains at rest, at their motion is due to (internal) forces of electrostatic attraction, which are conservative. No external force, what so ever is acting on the two particles

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