A block A of mass m₁ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m₂ is suspended. The coefficient of kinetic friction between the block and the table is  μ_k. When the block A is sliding on the table, the tension in the string is

1. (m₂+μ_km₁)g /(m₁+m₂)

2. (m₂-μ_km₁)g/(m₁+m₂)

3. m₁m₂(1+μ_k)g/(m₁+m₂)

4. m₁m₂(1-μ_k)g/(m₁+m₂)

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°, 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

A system consists of three masses m₁, m₂ and m₃ connected by a string passing over a pulley P. The mass $m_1$ 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. g(1-gμ)/9

2. 2gμ/3

3. g(1-2μ)/3

4. g(1-2μ)/2

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. 2ma/g+a

2. 2ma/g-a

3. ma/g+a

4. ma/g-a

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 lower half of the plane is given by

1. μ=1/tanθ

2. μ=2/tanθ

3. μ=2tanθ

4. μ=tanθ

A car of mass 1000 kg negotiates a banked curve of radius 90m on a frictionless road. If the banking angle is $45°$,the speed of the car is 

1. 20 $m{s}^{-1}$                                             2. 30 $m{s}^{-1}$

3. 5 $m{s}^{-1}$                                               4. 10 $m{s}^{-1}$

A car of mass \(m\) is moving on a level circular track of radius \(R\). If \(\mu_s\) represent the static friction between the road and tyres of the car, then the maximum speed of the car in circular motion is given by:

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 $1.0$ $\mathrm{m}/{\mathrm{s}}^2$. If $\mathrm{g}=10$ $\mathrm{m}/{\mathrm{s}}^2$, the tension in the supporting cable is:

1. 9680 N

2. 11000 N

3. 1200 N

4. 8600 N

Two masses of 10 kg and 20 kg respectively are connected by massless spring as shown in the figure. A force of 200 N acts on the 20 kg mass. At the instant shown the 10 kg mass has acceleration 12 $\mathrm{m}/{\mathrm{s}}^2$. What is the acceleration of 20 kg mass?

1. 12 $\mathrm{m}/{\mathrm{s}}^2$

2. 4 $\mathrm{m}/{\mathrm{s}}^2$

3. 10 $\mathrm{m}/{\mathrm{s}}^2$

4. zero

The slope of a smooth banked horizontal surface road is $p$. If the radius of the curve be $r$, the maximum velocity with which a car can negotiate the curve is given by

(a) $prg$

(b) $\sqrt{prg}$

(c) $p\mathit{/}rg$

(d) $\sqrt{p\mathit{/}rg}$