## SYSTEM OF PARTICLES AND ROTATIONAL MOTION QUIZ - 29

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: When a body dropped from a height explodes in mid air, its centre of mass keeps moving in vertically downward direction
Statement 2: Explosion occur under internal forces only. External force is zero
•  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)
Explosion is due to internal forces. As no external force is involved, the vertical downward motion of center of mass is not affected

Q2. Statement 1: The speed of whirlwind in a tornado is alarmingly high
Statement 2: If no external torque acts on a body, its angular velocity remains conserved
•  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

Q3. Statement 1: It is harder to open and shut the door if we apply force near the hinge
Statement 2: Torque is maximum at hinge of the door
•  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)
Torque = Force × perpendicular distance of line of action of force from the axis of rotation (d)
Hence for a given applied force, torque or true tendency of rotation will be high for large value of d. If distance d is smaller, then greater force is required to cause the same torque, hence it is harder to open or shut down the door by applying a force near the hinge

Q4. Statement 1: A uniform thin rod of length L is hinged about one of its ends and is free to rotate about the hinge without friction. Neglect the effect of gravity. A force F is applied at a distance x from hinge on the rod such that the force is always perpendicular to the rod. As value of x is increased from zero to L, the component of reaction by the hinge on the rod perpendicular to the length of rod increases
Statement 2: Under the conditions given in Statement 1 as x is increased from zero to L, the angular acceleration of the rod 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
(d)
As x increases, the required component of reaction decreases to zero and then increases (with direction reversed). Hence, statement I is false

Q5. Statement 1: A particle is moving on a straight line with a uniform velocity, its angular momentum is always zero
Statement 2: The momentum is zero when the particle moves with a uniform 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

Q6. Statement 1: A sphere is performing pure rolling on a rough horizontal with constant angular velocity. Frictional force acting on the sphere is zero
Statement 2: Velocity of contact is zero
•  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)
If angular velocity is constant, then frictional force acting on the sphere is zero. In case of pure rolling, velocity of contact point is zero

Q7. Statement 1: The total kinetic energy of a rolling solid sphere is the sum of translational and rotational kinetic energies
Statement 2: For all solid bodies total kinetic energy is always twice the translational kinetic energy
•  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 its center of mass, then the velocity of the center of mass remains constant
Statement 2: The linear 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
(d)
Velocity of center of mass of a body is constant when no external force acts on the body. If there is no external torque, it does not mean that no external force acts on it

Q9. Statement 1: A disc is rolling on a rough horizontal surface. The instantaneous speed of the point of contact during perfect rolling is zero with respect to the ground
Statement 2: The force of friction can help in achieving pure rolling condition
•  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

Q10. Statement 1: A judo fighter in order to throw his opponent on to the mattress he initially bend his opponent and then rotate him around his hip
Statement 2: As the mass of the opponent is brought closer to the fighter’s hip, the force required to throw the opponent is reduced
•  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)
Through bending weight of opponent is made to pass through the hip of judo fighter to make its torque zero

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