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 m2 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 m1, m2, and m3 connected by a string passing over a pulley P. The mass m1 hangs freely, and m2 and m3 are on a rough horizontal table (the coefficient of friction = μ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m1 is : (Assume m1 = m2 = m3 = m)

1. $\frac{g\left(1-g\mu \right)}{9}$

2. $\frac{2g\mu }{3}$

3. $\frac{g\left(1-2\mu \right)}{3}$

4. $\frac{g\left(1-2\mu \right)}{2}$

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
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
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 45o, 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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