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Q. No.Two solid spheres of mass \(m={{1}\over{2}}kg\) each are connected at the ends of a light rod as shown in the figure. The assembly rotates about axis AA'. Then moment of inertia of the assembly is equal to \({{x}\over{5}}kgm^{2}\) value of x is equal to:
1. 1.27
2. 3.14
3. 2.20
4. 2.91
Subtopic: Moment of Inertia |
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Level 2: 60%+
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R):
In the light of the above statements choose the correct answer from the options given below:
| Assertion (A): | Fan spins even after switch is in OFF. |
| Reason (R): | Fan in rotation has rotational inertia. |
In the light of the above statements choose the correct answer from the options given below:
| 1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
| 3. | (A) is true but (R) is false. |
| 4. | Both (A) and (R) are false. |
Subtopic: Moment of Inertia |
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Level 1: 80%+
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A body is rotating with kinetic energy, \(E.\) If the angular velocity of the body is increased to three times of the initial angular velocity then kinetic energy becomes \(nE.\) What would be the value of \(n?\)
1. \(3\)
2. \(7\)
3. \(9\)
4. \(5\)
1. \(3\)
2. \(7\)
3. \(9\)
4. \(5\)
Subtopic: Rotational Motion: Kinematics |
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Level 1: 80%+
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A force \(\overrightarrow {F}=-c \hat{k} \) is acting on a particle at the origin. The torque of this force about the point \((-2,3,0)\) is given by \(-c(A \hat{i}+B \hat{j}).\) If \({A \over B} = { x \over 2},\) then the value of \(x\) is:
1. \({2 \over 3}\)
2. \(3\)
3. \(1.5\)
4. \(1\)
1. \({2 \over 3}\)
2. \(3\)
3. \(1.5\)
4. \(1\)
Subtopic: Torque |
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Level 2: 60%+
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A uniform solid sphere is rolling without slipping on a horizontal surface. The ratio of translational kinetic energy to the total kinetic energy is 5/x. Find the value of x.
1. 2
2. 3
3. 5
4. 7
1. 2
2. 3
3. 5
4. 7
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Earth shrinks to \(1 \over 64\) times of its initial volume. Time period of earth rotation is found to be \( {24 \over x }~ \text {hrs.}\) The value of \(x\) is:
| 1. | \(16\) | 2. | \(20\) |
| 3. | \(4\) | 4. | \(10\) |
Subtopic: Angular Momentum |
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Level 3: 35%-60%
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What is the ratio of the radius of gyration of a solid sphere to that of a solid cylinder, given that both objects have the same mass and radius?
| 1. | \(\dfrac{2}{\sqrt{5}}\) | 2. | \(\dfrac{\sqrt{5}}{2}\) |
| 3. | \(\sqrt{\dfrac{2}{5}}\) | 4. | \(\dfrac{2}{\sqrt{3}}\) |
Subtopic: Moment of Inertia |
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Level 2: 60%+
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A body of mass 5 kg has the linear momentum of \(100 ~kg~ ms^{-1}\) and acted upon by the force of 2 N for 2 seconds, then change in kinetic energy in Joule is:
1. 100 J
2. 90 J
3. 204 J
4. 81.6 J
1. 100 J
2. 90 J
3. 204 J
4. 81.6 J
Subtopic: Linear Momentum |
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Level 2: 60%+
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A solid sphere and a ring have equal masses and equal radii of gyration. If the sphere is rotating about its diameter and the ring about an axis passing through and perpendicular to its plane, then the ratio of the radii is \(\sqrt{\dfrac{x}{2}}.\) The value of \(x\) is:
1. \(5\)
2. \(2\)
3. \(1\)
4. \(4\)
1. \(5\)
2. \(2\)
3. \(1\)
4. \(4\)
Subtopic: Moment of Inertia |
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Level 1: 80%+
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Momentum of a particle is increased by 50% by keeping its mass constant. Percentage increase in kinetic energy of particle is:
1. 50%
2. 125%
3. 100%
4. 200%
1. 50%
2. 125%
3. 100%
4. 200%
Subtopic: Linear Momentum |
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Level 1: 80%+
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