BITSAT Physics System Of Particles and Rotational Motion MCQs

Question: A thin but rigid semicircular wire frame of radius r is hinged at O and can rotate in its own vertical plane. A smooth peg P starts from O and moves horizontally with constant speed v₀, lifting the frame upward as shown in figure.

Find the angular velocity ω of the frame when its diameter makes an angle of 60° with the vertical :

• a) v₀/r
• b) v₀/2r
• c) 2_v0/r
• d) v₀r

Answer: v₀/r

Question: A circular disc of radius R and thickness  has moment inertia I about an axis passing through its centre perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of nertia of the sphere about its diameter is

• a) I
• b)

  

• c)

  

• d)

  

Answer:

Question: A thin rod of length 4l and mass 4m is bent at the points as shown in figure. What is the moment of inertia of the rod about the axis passes through point O and perpendicular to the plane of paper?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: An equilateral prism of mass m rests on a rough horizontal surface with coefficient of friction μ. A horizontal force F is applied on the prism as shown in the figure.

If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is –

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A particle of mass ‘m’ is projected with a velocity v making an angle of 30° with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height ‘h’ is

• a)

  

• b) zero
• c)

  

• d)

  

Answer:

Question: A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lower most point of the disc –

• a) velocity is v, acceleration is zero
• b) velocity is zero, acceleration is zero
• c) velocity is v, acceleration is v²/R
• d) velocity is zero, acceleration is v²/R

Answer: velocity is zero, acceleration is v²/R

Question: What is the moment of inertia of a solid sphere of density r and radius R about its diameter?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A wheel of radius R rolls on the ground with a uniform velocity v. The relative acceleration of topmost point of the wheel with respect to the bottom most point is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A constant torque of 31.4 N-m is exerted on a pivoted wheel. If angular acceleration of wheel is 4πrad/s² , then the moment of inertia of the wheel is

• a) 2.5 kg m²  
• b) 3.5 kg m²
• c) 4.5 kg m²
• d) 5.5 kg m²

Answer: 2.5 kg m² 

Question: The ratio of the accelerations for a solid sphere (mass ‘m’ and radius ‘R’) rolling down an incline of angle ‘θ’ without slipping and slipping down the incline without rolling is :

• a) 5 : 7
• b) 2 : 3
• c) 2 : 5
• d) 7 : 5

Answer: 5 : 7

Question: A system consists of three particles, each of mass m and located at (1, 1), (2, 2) and (3, 3). The coordinates of the centre of mass are

• a) (1, 1)
• b) (2, 2)
• c) (3, 3)
• d) (6, 6)

Answer: (2, 2)

Question: A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point that is directly above the centre of the face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to topple an edge is (assume that cube does not slide)

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to the plane with angular velocity ω. Another disc of same mass but half the radius is gently placed over it coaxially. The angular speed of the composite disc will be :

• a) (5/4) ω 
• b) (4/5) ω
• c) (2/5) ω
• d) (5/2) ω

Answer: (4/5) ω

Question: One solid sphere and disc of same radius are falling along an inclined plane without slipping. One reaches earlier than the other due to

• a) Different radius of gyration
• b) Different sizes
• c) Different friction
• d) Different moment of inertia

Answer: Different radius of gyration

Question: Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping,

• a) The heavier sphere reaches the bottom first
• b) The bigger sphere reaches the bottom first
• c) The two spheres reach the bottom together
• d) The information given is not sufficient to tell which sphere will reach the bottom first.

Answer: The two spheres reach the bottom together

Question: A thin wire of length L and uniform linear mass density r is bent into a circular loop with centre at O as shown in the figure. The moment of inertia of the loop about the axis XX' is :

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A smooth sphere A is moving on a friction less horizontal plane with angular speed ω and centre of mass velocity v. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision, their angular speeds are ω_A and ω_B, respectively. Then

• a) ω_A< ω_B
• b) ω_A= ω_B
• c) ω_A= ω
• d) ω_B= ω

Answer: ω_A= ω

Question: One solid sphere and disc of same radius are falling along an inclined plane without slipping. One reaches earlier than the other due to

• a) Different radius of gyration
• b) Different sizes
• c) Different friction
• d) Different moment of inertia

Answer: Different radius of gyration

Question: A system consists of three particles, each of mass m and located at (1, 1), (2, 2) and (3, 3). The coordinates of the centre of mass are

• a) (1, 1)
• b) (2, 2)
• c) (3, 3)
• d) (6, 6)

Answer: (2, 2)

Question: Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping,

• a) The heavier sphere reaches the bottom first
• b) The bigger sphere reaches the bottom first
• c) The two spheres reach the bottom together
• d) The information given is not sufficient to tell which sphere will reach the bottom first

Answer: The two spheres reach the bottom together