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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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Three identical spherical shells, each of mass \(m\) and radius \(r\) are placed as shown in the figure. Consider an axis \(XX'\), which is touching two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about the \(XX'\) axis is:

1. | \(\frac{11}{5}mr^2\) | 2. | \(3mr^2\) |

3. | \(\frac{16}{5}mr^2\) | 4. | \(4mr^2\) |

Subtopic: Moment of Inertia |

61%

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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An automobile moves on a road with a speed of \(54~\text{kmh}^{-1}.\) The radius of its wheels is \(0.45\) m and the moment of inertia of the wheel about its axis of rotation is \(3~\text{kg-m}^2.\) If the vehicle is brought to rest in \(15\) s, the magnitude of average torque transmitted by its brakes to the wheel is:

1. \(6.66~\text{kg-m}^2\text{s}^{-2}\)

2. \(8.58~\text{kg-m}^2\text{s}^{-2}\)

3. \(10.86~\text{kg-m}^2\text{s}^{-2}\)

4. \(2.86~\text{kg-m}^2\text{s}^{-2}\)

Subtopic: Torque |

73%

From NCERT

NEET - 2015

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A solid cylinder of mass \(50\) kg and radius \(0.5\) m is free to rotate about the horizontal axis. A massless string is wound around the cylinder with one end attached to it and the other end hanging freely.
The tension in the string required to produce an angular acceleration of \(2\) revolutions/s^{2} will be:

1. \(25\) N

2. \(50\) N

3. \(78.5\) N

4. \(157\) N

Subtopic: Rotational Motion: Dynamics |

51%

From NCERT

AIPMT - 2014

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A rod \(\mathrm{PQ}\) of mass \(M\) and length \(L\) is hinged at end \(\mathrm{P}\). The rod is kept horizontal by a massless string tied to point \(\mathrm{Q}\) as shown in the figure. When the string is cut, the initial angular acceleration of the rod is:

1. \(\frac{g}{L}\)

2. \(\frac{2g}{L}\)

3. \(\frac{2g}{3L}\)

4. \(\frac{3g}{2L}\)

Subtopic: Torque |

80%

From NCERT

AIPMT - 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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Two persons of masses \(55\) kg and \(65\) kg respectively, are at the opposite ends of a boat. The length of the boat is \(3.0\) m and weighs \(100\) kg. The \(55\) kg man walks up to the \(65\) kg man and sits with him. If the boat is in still water, the centre of mass of the system shifts by:

1. \(3.0\) m

2. \(2.3\) m

3. zero

4. \(0.75\) m

Subtopic: Center of Mass |

76%

From NCERT

AIPMT - 2012

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\(\mathrm{ABC}\) is an equilateral triangle with \(O\) as its centre. \(F_1\), \(F_2\)_{,} and \(F_3\) represent three forces acting along the sides \(\mathrm{AB},\) \(\mathrm{BC}\) and \(\mathrm{AC}\) respectively. If the total torque about \(O\) is zero, then the magnitude of \(F_3\) is:

1. \(F_1+F_2\)

2. \(F_1-F_2\)

3. \(\frac{F_1+F_2}{2}\)

4. \(2F_1+F_2\)

Subtopic: Torque |

76%

From NCERT

AIPMT - 2012

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The instantaneous angular position of a point on a rotating wheel is given by the equation,

$$\(\theta(t)=2t^{3}-6t^{2}\)

The torque on the wheel becomes zero at:

1. \(t=0.5\) s

2. \(t=0.25\) s

3. \(t=2\) s

4. \(t=1\) s

$$\(\theta(t)=2t^{3}-6t^{2}\)

The torque on the wheel becomes zero at:

1. \(t=0.5\) s

2. \(t=0.25\) s

3. \(t=2\) s

4. \(t=1\) s

Subtopic: Rotational Motion: Kinematics |

76%

From NCERT

AIPMT - 2011

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