# A uniform rod of length l and mass M is free to rotate in a vertical plane about A. The rod, initially in the horizontal position, is released. The initial angular acceleration of the rod is: (Moment of inertia of the rod about A is$\frac{{\mathrm{Ml}}^{2}}{3}$) 1. $$\frac{3g}{2l}$$ 2. $$\frac{2l}{3g}$$ 3. $$\frac{3g}{2l^2}$$ 4. $$\frac{mg}{2}$$

Subtopic:  Torque |
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The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc is:

1. $M{R}^{2}$

2. $\frac{2}{5}M{R}^{2}$

3. $\frac{3}{2}M{R}^{2}$

4. $\frac{1}{2}M{R}^{2}$

Subtopic:  Moment of Inertia |
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A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is at B, then: 1. ${L}_{A}>{L}_{B}$
2. ${L}_{A}={L}_{B}$
3. the relationship between LA and LB depends upon the slope of the line AB
4. ${L}_{A}<{L}_{B}$

Subtopic:  Angular Momentum |
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A wheel has an angular acceleration of 3.0 rad/s2 and an initial angular speed of 2.00 rad/s. In a time of 2 s, it has rotated through an angle (in radian) of:

1. 6
2. 10
3. 12
4. 4

Subtopic:  Rotational Motion: Kinematics |
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A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90o. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is:

1.  $\frac{{\mathrm{ML}}^{2}}{24}$

2.  $\frac{{\mathrm{ML}}^{2}}{12}$

3.  $\frac{{\mathrm{ML}}^{2}}{6}$

4.  $\frac{\sqrt{2}{\mathrm{ML}}^{2}}{24}$

Subtopic:  Moment of Inertia |
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The ratio of the radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, around their respective axes is:

1.

2.

3.

4.

Subtopic:  Moment of Inertia |
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Four identical thin rods, each of mass M and length l, form a square frame. The moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is:
1. $\frac{4}{3}M{l}^{2}$
2. $\frac{2}{3}M{l}^{2}$
3. $\frac{13}{3}M{l}^{2}$
4. $\frac{1}{3}M{l}^{2}$
Subtopic:  Moment of Inertia |
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Two bodies of mass 1 kg and 3 kg have position vectors  respectively. The centre of mass of this system has a position vector:
1. -2$\stackrel{^}{i}$+2$\stackrel{^}{k}$
2. -2$\stackrel{^}{i}$-$\stackrel{^}{j}$+$\stackrel{^}{k}$
3. 2$\stackrel{^}{i}$- $\stackrel{^}{j}$- 2$\stackrel{^}{k}$
4. -$\stackrel{^}{i}$+$\stackrel{^}{j}$+$\stackrel{^}{k}$

Subtopic:  Center of Mass |
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A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m are attached gently to the opposite ends of the diameter of the ring, the ring will then rotate with an angular velocity:

1. $\frac{\omega \left(M-2m\right)}{M+2m}$

2. $\frac{\omega M}{M+2m}$

3. $\frac{\omega \left(M+2m\right)}{M}$

4. $\frac{\omega M}{M+m}$

Subtopic:  Angular Momentum |
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If $$\vec F$$ is the force acting on a particle having position vector $$\vec r$$ and $$\vec \tau$$ be the torque of this force about the origin, then:

 1 $$\vec r\cdot\vec \tau\neq0\text{ and }\vec F\cdot\vec \tau=0$$ 2 $$\vec r\cdot\vec \tau>0\text{ and }\vec F\cdot\vec \tau<0$$ 3 $$\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau=0$$ 4 $$\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau\neq0$$
Subtopic:  Torque |
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