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SYSTEM OF PARTICLES AND ROTATIONAL MOTION QUIZ - 34

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: A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling motion)
       Statement 2: For perfect rolling motion, work done against friction 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)
Rolling occurs only on account of friction which is a tangential force capable of providing torque. When the inclined plane is perfectly smooth, body will simply slip under the effect of its own weight


Q2. Statement 1: Two Cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first 
       Statement 2: By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline
  •  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: 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: Product of mass of one particle and its distance from centre of mass is 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

Q4. Statement 1: If the earth shrinks (without change in mass) to half it’s present size, length of the day would become 6 hour 
       Statement 2: As size of earth change, its moment of inertia changes
  •  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


Q5. Statement 1: Radius of gyration of body is a constant quantity
       Statement 2: The radius of gyration of a body about an axis of rotation may be defined as the root mean square distance of the particle from the axis of rotation
  •  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: There are two propellers in a helicopter 
       Statement 2: Angular momentum is 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
(b)
Both, assertion and reason are true but the reason is not a correct explanation of the statement-1. Infact, if helicopter has only one propeller, the helicopter itself would turn in opposite direction to conserve the angular momentum


Q7. Statement 1: The centre of mass of an electron and proton, when released moves faster towards proton 
       Statement 2: Proton is heavier than electron
  •  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 position of centre of mass of electron and proton remains at rest. As their motion is due to internal force of electrostatic attraction, which is conservative force. No external force is acting on the two particles, therefore centre of mass remain at rest


Q8. Statement 1: A solid sphere is rolling on a rough horizontal surface. Acceleration of contact point is zero
       Statement 2: A solid sphere can roll on the smooth surface
  •  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: A disc is rolling on an inclined plane without slipping. The velocity of centre of mass is V. The other points on the disc lie on a circular arc having same speed as that of the centre of mass 
       Statement 2: When a disc is rolling on an inclined plane, the magnitude of velocities of all points from the contact point is the same, having distance equal to radius r
  •  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
NO SOLUTION

Q10. Statement 1: In rolling, all points of a rigid body have the same linear speed
         Statement 2: The rotational motion does not affect the linear velocity of rigid body

  •  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)
In rolling all points of rigid body have the same angular speed but different linear speed

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