Laws of Motion

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