A balloon with mass 'm' is descending down with an acceleration 'a' (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration 'a'?

1. $\frac{2ma}{g+a}$

2. $\frac{2ma}{g-a}$

3. $\frac{ma}{g+a}$

4. $\frac{ma}{g-a}$

Subtopic: Application of Laws |

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A body of mass (4m) is lying in the x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each other with equal speeds (u). The total kinetic energy generated due to explosion is:

1. $m{u}^{2}$

2. 1.5$m{u}^{2}$

3. 2$m{u}^{2}$

4. 3$m{u}^{2}$

Subtopic: Newton's Laws |

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The upper half of an inclined plane of inclination θ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of the plane is given by:

1. μ = 2/tanθ

2. μ = 2tanθ

3. μ = tanθ

4. μ = 1/tanθ

Subtopic: Friction |

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Three blocks with masses m, 2m, and 3m are connected by strings as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2m? (g is the acceleration due to gravity).

1. 2mg

2. 3mg

3. 6mg

4. zero

2. 3mg

3. 6mg

4. zero

Subtopic: Application of Laws |

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An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1kg moves with a speed of 12 ms^{–1} and the second part of mass 2 kg moves with 8 ms^{–1} speed. If the third part flies off with 4 ms^{–1} speed, then its mass is:

1. 5 kg

2. 7 kg

3. 17 kg

4. 3 kg

2. 7 kg

3. 17 kg

4. 3 kg

Subtopic: Newton's Laws |

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A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45^{o}, the speed of the car is:

1. 20 ms^{-1}

2. 30 ms^{-1}

3. 5 ms^{-1}

4. 10 ms^{-1}

Subtopic: Banking of Roads |

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A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration of 1.0 ${\mathrm{ms}}^{-2}$. If g = 10 ${\mathrm{ms}}^{-2}$, the tension in the supporting cable is

1. 9680 N

2. 11000N

3. 1200N

4. 8600 N

Subtopic: Application of Laws |

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A body of mass M hits normally a rigid wall with velocity v and bounces back with the same velocity. The impulse experienced by the body is:

1. 1.5Mv

2. 2Mv

3. zero

4. Mv

Subtopic: Newton's Laws |

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A block of mass m is in contact with the cart C as shown in the figure.

The coefficient of static friction between the block and the cart is $\mathrm{\mu}$. The acceleration $\mathrm{\alpha}$ of the cart that will prevent the block from falling satisfies:

1. $\mathrm{\alpha}>\frac{\mathrm{mg}}{\mathrm{\mu}}$

2. $\mathrm{\alpha}>\frac{\mathrm{g}}{\mathrm{\mu m}}$

3. $\mathrm{\alpha}\ge \frac{\mathrm{g}}{\mathrm{\mu}}$

4. $\mathrm{\alpha}<\frac{\mathrm{g}}{\mathrm{\mu}}$

Subtopic: Friction |

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A gramophone record is revolving with an angular velocity $\omega $. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is $\mu $. The coin will revolve with the record if:

1. $r=\mu g{\omega}^{2}$

2. $r<\frac{{\omega}^{2}}{\mu g}$

3. $r\le \frac{\mu g}{{\omega}^{2}}$

4. $r\ge \frac{\mu g}{{\omega}^{2}}$

Subtopic: Friction |

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