Question 1 of 16 What is the difference between moment of inertia of a rod about an axis passing through its one end and through its centre perpendicular to its length? A [latex]\frac{ML^2}{3}[/latex] B [latex]\frac{ML^2}{4}[/latex] C [latex]\frac{ML^2}{6}[/latex] D [latex]\frac{ML^2}{12}[/latex] 💡 Explanation [latex]I_{end} - I_{centre} = \frac{1}{3}ML^2 - \frac{1}{12}ML^2[/latex] = [latex]\frac{ML^2}{4}[/latex] Question 2 of 16 A merry-go-round is rotating with an angular speed ω. If a child sits in it, which of the following physical quantity is conserved? A kinetic energy B potential energy C linear momentum D angular momentum 💡 Explanation When the child sits on the merry-go-round, the moment of inertia I increases (mass moves farther from the axis). To keep L constant, the angular speed ω decreases. Thus, conserved quantity: Angular momentum. Question 3 of 16 The torque due to the gravitational force on a body about its centre of mass is A finite B infinite C zero D not measurable 💡 Explanation When taking torque about the centre of mass, the gravitational force acts through the same point, so τ=0. Question 4 of 16 If the rotational kinetic energy of a body is E and moment of inertia is I then angular momentum will be: A EI B [latex]\sqrt{2EI}[/latex] C [latex]\frac{E}{I}[/latex] D [latex]\sqrt{IE}[/latex] 💡 Explanation Rotational kinetic energy is given by: [latex]E = \frac{1}{2}I\omega^2[/latex] Angular momentum is: L = [latex]I\omega[/latex] [latex]\omega^2 = \frac{2E}{I}[/latex] [latex]\omega = \sqrt{\frac{2E}{I}}[/latex] Or, L = [latex]I\sqrt{\frac{2E}{I}} = \sqrt{2EI}[/latex] Question 5 of 16 A disc of moment of inertia I is rotating about an axis passing through its centre and perpendicular to its plane. If a small wax of mass m is dropped at distance r from the axis of rotation, then what will be the new moment of inertia of the disc? A I B [latex]I - mr^2[/latex] C [latex]I + mr^2[/latex] D [latex]\frac{I}{mr^2}[/latex] 💡 Explanation The moment of inertia of a point mass 'm' at distance 'r' from the axis is: [latex]I = mr^2[/latex] So, the new total moment of inertia becomes: [latex]I_{new} = I + mr^2[/latex] Question 6 of 16 The moment of inertia of a body of mass M about a given axis is I. What is the radius of gyration? A [latex]\dfrac{I}{M}[/latex] B [latex]IM[/latex] C [latex]\sqrt{\dfrac{I}{M}}[/latex] D [latex]\sqrt{IM}[/latex] 💡 Explanation Radius of gyration k is defined by [latex]I = Mk^2[/latex], so: [latex]k = \sqrt{\frac{I}{M}}[/latex] Question 7 of 16 A body applied with constant torque changes the angular momentum [latex]L_o[/latex] to final angular momentum [latex]4L_o[/latex] in 3 sec., then the torque is A [latex]3L_o[/latex] B [latex]L_o[/latex] C [latex]4L_o[/latex] D [latex]2L_o[/latex] 💡 Explanation Torque is the rate of change of angular momentum: [latex]\tau = \frac{\Delta L}{\Delta t} = \frac{4L_o - L_o}{3} = \frac{3L_o}{3} = L_o[/latex] Question 8 of 16 Which quantity in rotational motion is analogous to force in linear motion? A Torque B Moment of inertia C Angular velocity D Angular momentum 💡 Explanation Just as force causes linear acceleration ([latex]F=ma[/latex]), torque causes angular acceleration ([latex]\tau = I\alpha[/latex]), making torque the rotational analogue of force. Question 9 of 16 When the torque acting upon a system is zero, which of the following will be constant? A Force B Linear momentum C Angular momentum D Angular acceleration 💡 Explanation Since [latex]\tau = \dfrac{dL}{dt}[/latex], if [latex]\tau = 0[/latex], then [latex]\dfrac{dL}{dt}=0[/latex], meaning angular momentum L remains constant (law of conservation of angular momentum). Question 10 of 16 When torque acting upon a system is zero, which of the following will be constant? A Force B Linear momentum C Angular momentum D Impulse 💡 Explanation Since [latex]\tau = \dfrac{dL}{dt}[/latex], if [latex]\tau = 0[/latex], then [latex]\dfrac{dL}{dt}=0[/latex], meaning angular momentum L remains constant. zero net torque implies angular momentum is conserved. Question 11 of 16 The spokes are used in bicycle wheel to A increase frictional force B decrease frictional force C decrease moment of inertia D increase moment of inertia 💡 Explanation Spokes replace what would otherwise be a solid disc, concentrating less mass in the wheel while maintaining its shape and strength. This reduces the wheel's moment of inertia, making it easier to accelerate and decelerate (pedal and brake). Question 12 of 16 In rotational motion, the physical quantity that imparts angular acceleration is, A Force B Torque C Moment of inertia D Angular momentum 💡 Explanation Just as force produces linear acceleration, torque produces angular acceleration, following the relation [latex]\tau = I\alpha[/latex]. Question 13 of 16 If L represents momentum, I represents moment of inertia, then [latex]\dfrac{L^2}{2I}[/latex] represents, A Rotational kinetic energy B Torque C Power D Potential energy 💡 Explanation Rotational kinetic energy is [latex]KE_{rot} = \dfrac{1}{2}I\omega^2[/latex]. Since [latex]L = I\omega \implies \omega = \dfrac{L}{I}[/latex]: [latex]KE_{rot} = \frac{1}{2}I\left(\frac{L}{I}\right)^2 = \frac{L^2}{2I}[/latex] Question 14 of 16 What is factor affecting radius of gyration of a body? A Angular speed B Axis of rotation C Angular acceleration D Acceleration due to gravity 💡 Explanation Radius of gyration depends on how the mass of a body is distributed relative to the chosen axis of rotation. The same body will have a different radius of gyration for different axes, since [latex]I = Mk^2[/latex] and I itself depends on the axis chosen. Question 15 of 16 What is the product of moment of inertia and angular acceleration called? A Angular momentum B Torque C Angular velocity D Force 💡 Explanation Torque is defined by the rotational analogue of Newton's second law: [latex]\tau = I\alpha[/latex] where I is moment of inertia and α is angular acceleration. Question 16 of 16 The product of moment of inertia and angular velocity gives A Force B Angular acceleration C Torque D Angular momentum 💡 Explanation Angular momentum is defined as: [latex]L = I\omega[/latex] where I is the moment of inertia and ω is the angular velocity. ← Prev Check Next → Finish & See Score 0 of 16 checked ← Back 1 / 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
