Laws of Motion

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 = ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m1 is (Assume m1 = m2 = m3 = m) [figure]

1. g(1 - g )9
2. 2g 3
3. g(1 - 2 )3
4. g(1 - 2 )2

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 zero to 8 s is : [figure]

1. 24 N s
2. 20 N s
3. 12 N s
4. 6 N s

A body of mass (4m) is lying in 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 (v). The total kinetic energy generated due to explosion is :

1. mv2
2. 32mv2
3. 2mv2
4. 4mv2

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 1 kg moves with a speed of 12 m s-1 and the second part of mass 2 kg moves with 8 m s-1 speed. If the third part flies off with 4 m s-1 speed, then its mass is :

1. 7 kg
2. 17 kg
3. 3 kg
4. 5 kg

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 upwards at constant speed v. What is the net force on the block of mass 2m ? (g is the acceleration due to gravity) [figure]

1. 3mg
2. 6mg
3. zero
4. 2mg

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A bob is suspended from the roof of the car by a light wire of length 1.0 m. The angle made by the wire with the vertical is

1. 3
2. 6
3. 4
4. 0

A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s. Each bullet has a mass of 10 g with a muzzle velocity of 800 m s-1. The final velocity acquired by the person and the average force exerted on the person are :

1. -0.08 m s-1, 16 N
2. -0.8 m s-1, 16 N
3. -1.6 m s-1, 16 N
4. -1.6 m s-1, 8 N

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

1. s mRg
2. Rg s
3. mRg s
4. s Rg

A car of mass 1000 kg negotiates a banked curve of radius 90 m 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 conveyor belt is moving at a constant speed of 2 m s-1. A box is gently dropped on it. The coefficient of friction between them is = 0.5. The distance that the box will move relative to belt before coming to rest on it, taking g = 10 m s-2, is

1. 0.4 m
2. 1.2 m
3. 0.6 m
4. zero