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SYSTEM OF PARTICLES AND ROTATIONAL MOTION QUIZ - 29

Dear Readers,

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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