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Rotational Motion Quiz-17

Dear Readers,

As per analysis for previous years, it has been observed that students preparing for NEET find Physics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Biology due to their medical background. Furthermore, sections such as Physics are dominantly based on theories, laws, numerical in comparison to a section of Biology which is more of fact-based, life sciences, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced. .

Q1. The position of a particle is given by r="i" ̂ + 2"j" ̂ - k ̂ and its linear momentum is given by p = 3 "i" ̂ + 4 "j" ̂ - 2 +k ̂ then its angular momentum, about the origin is perpendicular to?
  •  yz-plane
  •  z-axis
  •  y-axis
  •  x-axis
Solution


L has components along –y axis and –z axis. The angular momentum is in y-z plane ie., perpendicular to x-axis.


Q2. If the earth is treated as a sphere of radius R and mass M; its angular momentum about axis of rotation with period T is?
  •  (πMR3)/T
  •  (MR2 π)/T
  •  (2πMR3)/5T
  •  (4πMR2)/5T
Solution
Angular momentum is given by J=Iω=((2MR2)/5)ω =(2MR2)/5×2π/T=(4πMR2)/5T

Q3. A pulley of radius 2m is rotated about its axis by a force F=(20t-5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10kg m2, the number of rotations made by the pulley before its direction of motion if reversed, is?
  •  Less than 3
  •  More than 3 but less than 6
  •  More than 6 but less than 9
  •  More than 9
Solution



Q4. Three point masses, each of mass m are placed at the corners of an equilateral triangle of side l. Moment of inertia of this system about an axis along one side of triangle is?
  •  3 ml2
  •  3/2 ml2
  •  ml2
  •  3/4 ml2
Solution
Distance of corner mass from opposite side r=√(l2-(l/2)2 )=√3/2 l I=mr2=3/4 ml2

Q5. A wheel is rolling along the ground with a speed of 2 ms-1. The magnitude of the velocity of the points at the extremities of the horizontal diameter of the wheel is equal to?
  •  2√10 ms-1
  •  2√3 ms-1
  •  2√2 ms-1
  •  2 ms-1
Solution
 vt= velocity due to translator motion vR= velocity due to rotational motion 

vN=√(vt2+vR2 )=√(v2+v2 )=√2v=2√2 m/s


Q6. If the angular momentum of a rotating body about a fixed axis is increased by 10%. Its kinetic energy will be increased by?
  •  10%
  •  20%
  •  21%
  •  5%
Solution
Kinetic energy K=J2/2I where J is angular momentum and I the moment of inertia. ∴K1=J2/2I , K2=(J+10/100 J)2/2I ∴K1/K2 =(100)2/(110)2 =100/121 % change =(K2-K1)/K1 =K2/K1 -1 =121/100-1=21%

Q7. The diameter of a flywheel is increased by 1%. Increase in its moment of inertia about the central axis is?
  •  1%
  •  0.5%
  •  2%
  •  4%
Solution
I=MR2 ∴ log⁡I=log⁡M+2log⁡R Differentiating, we get dI/I=0+2dR/R ∴ dI/I×100=2(dR/R)×100 =2×1/100×100=2%

Q8. A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now the platform is given an angular velocity ω0. When the tortoise moves along a chord of the platform with a constant velocity (w.r.t. the platform), the angular velocity of the platform will vary with the time t as?
  •  

  •  

  •  

  •  

Solution
As there is no external torque, angular momentum will remain constant. When the tortoise moves from A to C, figure, moment of inertia of the platform and tortoise decreases. Therefore, angular velocity of the system increases. When the tortoise moves from C to B, moment of inertia increases. Therefore, angular velocity decreases 

If, M=mass of platform R=radius of platform m=mass of tortoise moving along the chord AB a=perpendicular distance of O from AB Initial angular momentum, I1=mR2+(MR2)/2 At any time t, let the tortoise reach D moving with velocity v ∴ AD=vt AC=√(R2-a2 ) As DC=AC-AD=(√(R2-a2 )-vt) ∴ OD=r=a2+[√(R2-a2 )-vt]2 Angular momentum at time t I2=mr2+(MR2)/2 As angular momentum is conserved ∴ I1 ω0=I2 ω(t) This shows that variation of ω(t) with time is nonlinear. Choice (c) is correct


Q9. A solid sphere is rotating about a diameter at an angular velocity ω. If it cools so that its radius reduces to 1/n of its original value, its angular velocity becomes?
  •  ω/n
  •  ω/n2
  •  
  •  n2 ω
Solution
On applying law of conservation of angular momentum I1 ω1=I2 ω2 For solid sphere, I=2/5 mr2⇒2/5 mr12 ω1=2/5 mr22 ω2 r2 ω=(r/n)2 ω2⇒ω2=n2 ω

Q10. Three identical spheres of mass M each are placed at the corners of an equilateral triangle of side 2 m. Taking one of the corners as the origin, the position vector of the centre of mass is?
  •  √3(i ̂-j ̂)
  •  i ̂/√3+j ̂
  •  i ̂+j ̂/3
  •  i ̂+j ̂/√3
Solution


=(M×0+M×1+M×2)/(M+M+M)=1

=(M×0+M(2 sin⁡60°)+M×0)/(M+M+M) =(√3 M)/3M=1/√3 ∴ Position vector of centre of mass is (i ̂+1/√3 j ̂ ) .

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Rotational Motion Quiz 17
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