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. \(40\)

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

3. $\frac{M\omega}{M+2m}$

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

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. | \(L_A<L_B\) |

Subtopic: Angular Momentum |

69%

From NCERT

AIPMT - 2007

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