Laws of Motion · Question 43

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