A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30^{o}, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively:

1. 0.6 and 0.6

2. 0.6 and 0.5

3. 0.5 and 0.6

4. 0.4 and 0.3

Subtopic: Friction |

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Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius $\frac{r}{2}$ and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is-

1. 2

2. 3

3. 4

4. 1

Subtopic: Uniform Circular Motion |

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Three blocks A, B, and C of masses 4 kg, 2 kg, and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied to the 4kg block, then the contact force between A and B is:

1. 2 N

2. 6 N

3. 8 N

4. 18 N

Subtopic: Application of Laws |

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A block A of mass ${\mathrm{m}}_{1}$ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of the table and from its other end, another block B of mass m_{2} is suspended. The coefficient of kinetic friction between block A and the table is ${\mathrm{\mu}}_{\mathrm{k}}$. When block A is sliding on the table, the tension in the string is:

1. $\frac{\left({\mathrm{m}}_{2}+{\mathrm{\mu}}_{\mathrm{k}}{\mathrm{m}}_{1}\right)\mathrm{g}}{\left({\mathrm{m}}_{1}+{\mathrm{m}}_{2}\right)}$

2. $\frac{\left({\mathrm{m}}_{2}-{\mathrm{\mu}}_{\mathrm{k}}{\mathrm{m}}_{1}\right)\mathrm{g}}{\left({\mathrm{m}}_{1}+{\mathrm{m}}_{2}\right)}$

3. $\frac{{\mathrm{m}}_{1}{\mathrm{m}}_{2}\left(1-{\mathrm{\mu}}_{\mathrm{k}}\right)\mathrm{g}}{\left({\mathrm{m}}_{1}+{\mathrm{m}}_{2}\right)}$

4. $\frac{{\mathrm{m}}_{1}{\mathrm{m}}_{2}\left(1+{\mathrm{\mu}}_{\mathrm{k}}\right)}{{\mathrm{m}}_{1}+{\mathrm{m}}_{2}}\mathrm{g}$

Subtopic: Friction |

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A system consists of three masses m_{1}, m_{2,} and m_{3} connected by a string passing over a pulley P. The mass m_{1} hangs freely, and m_{2} and m_{3} are on a rough horizontal table (the coefficient of friction = μ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m_{1} is : (Assume m_{1} = m_{2} = m_{3} = m)

1. $\frac{g(1-g\mu )}{9}$

2. $\frac{2g\mu}{3}$

3. $\frac{g(1-2\mu )}{3}$

4. $\frac{g(1-2\mu )}{2}$

Subtopic: Friction |

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The force 'F' acting on a particle of mass 'm' is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from 0 to 8 s is :

1. 24 Ns

2. 20 Ns

3. 12Ns

4. 6 Ns

Subtopic: Newton's Laws |

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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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