A mass $$m$$ moves in a circle on a smooth horizontal plane with velocity $$v_0$$ at a radius $$R_0$$. The mass is attached to a string that passes through a smooth hole in the plane, as shown.

The tension in the string is increased gradually and finally, $$m$$ moves in a circle of radius $$\frac{R_0}{2}$$. The final value of the kinetic energy is:
1. $$m v_0^2$$
2. $$\frac{1}{4} m v_0^2$$
3. $$2 m v_0^2$$
4. $$\frac{1}{2} m v_0^2$$

Subtopic:  Angular Momentum |
59%
From NCERT
NEET - 2015
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A force $\stackrel{}{}$$$\vec{F}=\alpha \hat{i}+3 \hat{j}+6 \hat{k}$$ is acting at a point  $$\vec{r}=2 \hat{i}-6 \hat{j}-12 \hat{k}$$. The value of $$\alpha$$ for which angular momentum about the origin is conserved is:
1. $$-1$$
2. $$2$$
3. zero
4. $$1$$

Subtopic:  Angular Momentum |
68%
From NCERT
NEET - 2015
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Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc $$D_1$$ has a $$2$$ kg mass and $$0.2$$ m radius and an initial angular velocity of $$50~\text{rads}^{-1}$$. Disc $$D_2$$ has a $$4$$ kg mass, $$0.1$$ m radius and an initial angular velocity of $$200$$ rad s–1. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s –1) of the system is:
1. $$60$$
2. $$100$$
3. $$120$$
4. $$40$$
Subtopic:  Angular Momentum |
76%
From NCERT
NEET - 2013
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When a mass is rotating in a plane about a fixed point, its angular momentum is directed along:

 1 a line perpendicular to the plane of rotation 2 the line making an angle of $$45^{\circ}$$ to the plane of rotation 3 the radius 4 the tangent to the orbit

Subtopic:  Angular Momentum |
75%
From NCERT
AIPMT - 2012
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A circular platform is mounted on a frictionless vertical axle. Its radius $$R = 2~\text{m}$$ and its moment of inertia about the axle is $$200~\text{kg m}^2$$. It is initially at rest. A $$50~\text{kg}$$ man stands on the edge of the platform and begins to walk along the edge at the speed of $$1~\text{ms}^{-1}$$ relative to the ground. The time taken by man to complete one revolution is:
1. $$\frac{3\pi}{2}\text{s}$$
2. $$2\pi~\text{s}$$
3. $$\frac{\pi}{2}\text{s}$$
4. $$\pi~\text{s}$$

Subtopic:  Angular Momentum |
64%
From NCERT
AIPMT - 2012
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A circular disk of a moment of inertia $$\mathrm{I_t}$$ is rotating in a horizontal plane, about its symmetric axis, with a constant angular speed $$\omega_i.$$ Another disk of a moment of inertia $$\mathrm{I_b}$$ is dropped coaxially onto the rotating disk. Initially, the second disk has zero angular speed. Eventually, both the disks rotate with a constant angular speed $$\omega_f.$$ The energy lost by the initially rotating disc due to friction is:
1. $$\frac{1}{2} \frac{\mathrm{I}_{\mathrm{b}}^2}{\left(\mathrm{I}_{\mathrm{t}}+\mathrm{I}_{\mathrm{b}}\right)} \omega_{\mathrm{i}}^2$$

2. $$\frac{1}{2} \frac{\mathrm{I}_{\mathrm{t}}^2}{\left(\mathrm{I}_{\mathrm{t}}+\mathrm{I}_{\mathrm{b}}\right)} \omega_{\mathrm{i}}^2$$

3. $$\frac{1}{2} \frac{\mathrm{I}_{\mathrm{b}}-\mathrm{I}_{\mathrm{t}}}{\left(\mathrm{I}_{\mathrm{t}}+\mathrm{I}_{\mathrm{b}}\right)} \omega_{\mathrm{i}}^2$$

4. $$\frac{1}{2} \frac{\mathrm{I}_{\mathrm{b}} \mathrm{I}_{\mathrm{t}}}{\left(\mathrm{I}_{\mathrm{t}}+\mathrm{I}_{\mathrm{b}}\right)} \omega_{\mathrm{i}}^2$$

Subtopic:  Angular Momentum |
72%
From NCERT
AIPMT - 2010
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A thin circular ring of mass $$M$$ and radius $$r$$ is rotating about its axis with constant angular velocity ω. Two objects each of mass $$m$$ are attached gently to the opposite ends of the diameter of the ring. The ring now rotates with angular velocity given by:

1. $\frac{2M\omega }{M+2m}$

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

3. $\frac{M\omega }{M+2m}$

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

Subtopic:  Angular Momentum |
84%
From NCERT
AIPMT - 2010
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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 $$\frac{\omega(M-2 m)}{M+2 m}$$ 2 $$\frac{\omega M}{M+2 m}$$ 3 $$\frac{\omega(M+2 m)}{M}$$ 4 $$\frac{\omega M}{M+m}$$
Subtopic:  Angular Momentum |
83%
From NCERT
AIPMT - 2009
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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 the origin $$O$$ is $$L_A$$ when it is at $$A$$ and $$L_B$$ when it is at $$B,$$ then:

 1 $$L_A>L_B$$ 2 $$L_A=L_B$$ 3 the relationship between $$L_A$$ and $$L_B$$ depends upon the slope of the line $$AB.$$ 4 \(L_A
Subtopic:  Angular Momentum |
69%
From NCERT
AIPMT - 2007
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