Two bodies of mass, 4 kg and 6 kg, are tied to the ends of a massless string. The string passes over a pulley, which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is:

1. g/2

2. g/5

3. g/10

4. g

Subtopic: Application of Laws |

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A point mass 'm' is moved in a vertical circle of radius 'r' with the help of a string. The velocity of the mass is $\sqrt{7\mathrm{gr}}$ at the lowest point. The tension in the string at the lowest point is:

1. 6mg

2. 7mg

3. 8mg

4. 1mg

Subtopic: Non Uniform Vertical Circular Motion |

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Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is 0.05.

( $g=10m/{s}^{2},$ mass of the string is negligible and no other friction exists ).

1. 1.25 $m/{s}^{2}$

2. 1.50 $m/{s}^{2}$

3. 1.66 $m/{s}^{2}$

4. 1.00 $m/{s}^{2}$

Subtopic: Friction |

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A body of mass m is kept on a rough horizontal surface (coefficient of friction= $\mu $). A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by $\overrightarrow{F}$, where:

1. $\left|\overrightarrow{F}\right|=mg+\mu mg$

2. $\left|\overrightarrow{F}\right|=\mu mg$

3. $\left|\overrightarrow{F}\right|\le mg\sqrt{1+{\mu}^{2}}$

4. $\left|\overrightarrow{F}\right|=mg$

Subtopic: Friction |

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A truck is stationary and has a bob suspended by a light string in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of a. In the frame of the truck, the pendulum will tilt:

1. to the left and angle of inclination of the pendulum with the vertical is ${\mathrm{sin}}^{-1}\left(\frac{a}{g}\right)$

2. to the left and angle of inclination of the pendulum with the vertical is ${\mathrm{cos}}^{-1}\left(\frac{a}{g}\right)$

3. to the left and angle of inclination of the pendulum with the vertical is ${\mathrm{tan}}^{-1}\left(\frac{a}{g}\right)$

4. to the left and angle of inclination of the pendulum with the vertical is ${\mathrm{tan}}^{-1}\left(\frac{g}{a}\right)$

Subtopic: Application of Laws |

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A car of mass m is moving on a level circular track of radius R. If ${\mu}_{s}$ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by -

1. $\sqrt{Rg/{\mu}_{s}}$

2. $\sqrt{mRg/{\mu}_{s}}$

3. $\sqrt{{\mu}_{s}Rg}$

4. $\sqrt{{\mu}_{s}mRg}$

Subtopic: Friction |

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A conveyor belt is moving at a constant speed of 2 m/s. A box is gently dropped on it. The coefficient of friction between them is µ = 0.5. The distance that the box will move relative to the belt before coming to rest on it, taking g = 10 ms^{–2} is:

1. 0.4 m

2. 1.2 m

3. 0.6 m

4. Zero

Subtopic: Friction |

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A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will

1. decrease by a factor of 2

2. remain constant

3. increase by a factor of 2

4. increase by a factor of 4

Subtopic: Non Uniform Vertical Circular Motion |

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Two masses as shown are suspended from a massless pulley. Calculate the acceleration of the system when masses are left free.

1. 2g/3

2. g/3

3. g/9

4. g/7

Subtopic: Application of Laws |

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A body of mass 3 kg hits a wall at an angle of 60º & returns at the same angle. The impact time was 0.2 s. Calculate the force exerted on the wall.

1. 150 $\sqrt{3}$ N

2. 50 $\sqrt{3}$ N

3. 100 N

4. 75 $\sqrt{3}$ N

Subtopic: Application of Laws |

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