Rotational Motion Quiz 13

Rotational Motion Quiz-13

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. Out of the given bodies (of same mass) for which the moment of inertia will be maximum about the axis passing through its centre of gravity and perpendicular to its plane?

•  Disc of radius a
•  Ring of radius a
•  Square lamina of side 2a
•  Four rods of length 2a making a square

Solution
For disc, I=1/2 ma² For ring, I=ma² For square of side 2a=M/12 [(2a)²+(2a)² ]=2/3 Ma² For square of rod of length 2a I=4[M (2a)²/12+Ma² ]=16/3 Ma² Hence, moment of inertia is maximum for square of four rods

Q2. A ring of mass 10 kg and diameter 0.4 m is rotated about its axis. If it makes 2100 revolutions per minute, then its angular momentum will be?

•  44 kg ×m²/s
•  88 kg ×m²/s
•  4.4 kg ×m²/s
•  0.4 kg ×m²/s

Solution
I=mr²=10×(0.2)²=0.4kg-m² ω=2π n=2π×2100/60 rad/s ∴L=Iω=(0.4×2π×210)/6=88kg-m²/s

Q3. The moment of inertia of a body does not depend upon?

•  The angular velocity of the body
•  The mass of the body
•  The distribution of mass in the body
•  The axis of rotation of the body

Solution
The angular velocity of the body

Q4. A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω. Its centre of mass rises to maximum height of?

•  1/3 (l² ω²)/g
•  1/6 lω/g
•  1/2 (l² ω²)/g
•  1/6 (l² ω²)/g

Solution
TE_i=TE_r 1/2 Iω²=mgh 1/2×1/3 ml² ω²=mgh ⇒h=1/6 (l² ω²)/g

Q5. A particle is projected with a speed v at 45⁰ with the horizontal. The magnitude of angular momentum of the projectille about the point of projection when the particle is at its maximum height h is ?

•  Zero
•  mvh²/√2
•  (mv² h)/√2
•  (mv² h)/√2

Solution
 When a particle is projected with a speed v at 45° with the horizontal then velocity of the projectile at maximum height. v^'=v cos⁡45°=v/√2 Angular momentum of the projectile about the point of projection =mv'h =m v/√2 h=mvh/√2

Q6. Two rigid bodies A and B rotate with rotational kinetic energies E_A and E_B respectively. The moments of inertia of A and B about the axis of rotation are I_A and I_B respectively. If I_A=I_B/4 and E_A=100 E_B the ratio of angular momentum (L_A) of A to the angular momentum (L_B) of B is?

•  25
•  5/4
•  5
•  1/4

Solution
Rotational kinetic energy E=L²/2I ∴L=√2EI ⇒L_A/L_B =√(E_A/E_B ×I_A/I_B )=√(100×1/4)=5 .

Q7. A 1m long rod has a mass of 0.12 kg. What is the moment of inertia about an axis passing through the centre and perpendicular to the length of rod?

•  0.01kg-m²
•  0.001kg-m²
•  1kg-m²
•  10kg-m²

Solution
I= (ML²)/12=(0.12×1²)/12=0.01kg-m²

Q8. ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. I_AB,I_BC,I_CA are the moments of inertia of the plate about AB,BC,CA respectively. Which one of the following relations is correct?

•  I_CA is maximum
•  I_AB>I_BC
•  I_BC>I_AB
•  I_AB+I_BC=I_CA

Solution
Distribution of mass about BC axis is more than that about AB axis, i.e. radius of gyration about BC axis is more than that about AB axis i.e.K_BC>K_AB ∴I_BC>I_AB>I_CA

Q9. A circular turn table has a block of ice placed at its centre. The system rotates with an angular speed ω about an axis passing through the centre of the table. If the ice melts on its own without any evaporation, the speed of rotation of the system?

•  Becomes zero
•  Remains constant at the same value ω
•  Increases to a value greater than ω
•  Decreases to a value less than ω

Solution
Melting of ice produces water which will spread over larger distance away from the axis of rotation. This increases the moment of inertia so angular velocity decreases

Q10. A loded spring gun of mass M fires a shot of mass m with a velocity v at an angle of elevation θ. The gun was initially at rest on a horizontal frictionless surface. After firing, the centre of mass of gun-shot system ?

•  Moves with a velocity mv/M
•  Moves with a velocity mv/(M cos⁡θ ) in the horizontal direction
•  Remain at rest
•  Moves with velocity ((M-m)v)/((M+m)) in the horizontal direction

Solution
Since gun-shot system is an isolated closed system, its centre of mass must remain at rest.