Laws of Motion

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. 2mag+a
2. 2mag-a
3. mag+a
4. mag-a

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

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 m/s2. If g = 10 m s-2, the tension in the supporting cable is

1. 8600 N
2. 9680 N
3. 11000 N
4. 1200 N

A body of mass M hits normally a rigid wall with velocity V and bounces back with the same velocity. The impulse experienced by the body is

1. MV
2. 1.5 MV
3. 2MV
4. zero

A block of mass m is in contact with the cart C as shown in the figure. The coefficient of static friction between the block and the cart is . The acceleration of the cart that will prevent the block from falling satisfies [figure]

1. > mg
2. > g m
3. g
4. < g

A gramophone record is revolving with an angular velocity . A coin is placed at a distance r from the centre of the record. The static coefficient of friction is . The coin will revolve with the record if

1. r = 2
2. r < 2
3. r 2
4. r 2

A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be

1. 9.9 m
2. 10.1 m
3. 10 m
4. 20 m

The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N, then its acceleration is:

1. 4 m s-2 upwards
2. 4 m s-2 downwards
3. 14 m s-2 upwards
4. 30 m s-2 downwards

A body, under the action of a force F = 6 i - 8 j + 10 k, acquires an acceleration of 1 m s-2. The mass of this body must be

1. 10 kg
2. 20 kg
3. 10 2 kg
4. 2 10 kg

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of 12 m s-1 and 2 kg second part moving with a velocity 8 m s-1. If the third part flies off with a velocity of 4 m s-1, its mass would be:

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

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between

1. 16 m/s and 17 m/s
2. 13 m/s and 14 m/s
3. 14 m/s and 15 m/s
4. 15 m/s and 16 m/s

Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be :

1. Mv2 newton
2. zero
3. Mv newton
4. 2 Mv newton

[figure] Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is

1. 34 N
2. 3 N
3. 0.5 N
4. 1.5 N

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is :

1. 40 m s-1
2. 120 m s-1
3. 100 m s-1
4. 80 m s-1

A block B is pushed momentarily along a horizontal surface with an initial velocity V. If μ is the coefficient of sliding friction between B and the surface, block B will come to rest after a time [figure]

1. g /V
2. g/V
3. V/g
4. V/(g )

A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of 30 with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for 0.25 seconds, the average force acting on the wall is :

1. 96 N
2. 48 N
3. 24 N
4. 12 N

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity . The force exerted by the liquid at the other end is

1. ML2 22
2. ML 22
3. ML2 2
4. ML 2

A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 m s-1. The kinetic energy of the other mass is :

1. 324 J
2. 486 J
3. 256 J
4. 524 J

A block of mass m is placed on a smooth wedge of inclination . The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block will be (g is acceleration due to gravity)

1. mg
2. mg
3. mg
4. mg/

The coefficient of static friction, s, between block A of mass 2 kg and the table as shown in the figure is 0.2. What would be the maximum mass value of block B so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless. (g = 10 m/s2) [figure]

1. 2.0 kg
2. 4.0 kg
3. 0.2 kg
4. 0.4 kg

A man weighs 80 kg. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of 5 m/s2. What would be the reading on the scale ? (g = 10 m/s2)

1. zero
2. 400 N
3. 800 N
4. 1200 N