The motion of a particle of mass m is described by y = $\mathrm{ut} + \frac{1}{2}{\mathrm{gt}}^2$. Force acting on the particle is: 

1.  3mg

2.  mg

3.  $\frac{\mathrm{mg}}{2}$

4.  2mg

A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of 12 m/s. If the mass of the ball is 0.15 kg, impulse imparted to the ball is:

(Assume linear motion of the ball)

1.  0.15 N s

2.  3.6 N s

3.  36 N s

4.  0.36 N s

Two identical billiard balls strike a rigid wall with the same speed but at different angles, and get reflected without any change in speed, as shown in fig. The ratio of the magnitudes of impulses imparted to the balls by the wall is:

1.  $2:3$

2.  $\sqrt{3}:2$

3.  $2:\sqrt{3}$

4.  $1:1$

See the figure given below. A mass of 6 kg is suspended by a rope of length 2 m from the ceiling. A force of 50 N is applied at the mid-point P of the rope in the horizontal direction, as shown. What angle does the rope make with the vertical in equilibrium? (Take g = 10 ${\mathrm{ms}}^{-2}$). Neglect the mass of the rope.

1.  ${90}^0$

2.  ${30}^0$

3.  ${40}^0$

4.   $0^0$

Determine the maximum acceleration of the train in which a box lying on its floor will remain stationary, given that the coefficient of static friction between the box and the train’s floor is 0.15.

2.  0.5 $\mathrm{m}/{\mathrm{s}}^2$

3.  2.5 $\mathrm{m}/{\mathrm{s}}^2$

4.   1.5 $\mathrm{m}/{\mathrm{s}}^2$

See the figure given below, a mass of 4 kg rests on a horizontal plane. The plane is gradually inclined until at an angle θ = 15° with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?

2.  0.53

3.  0.23

4.  0.25

What is the acceleration of the block and tension in the string of the block and trolley system shown in a figure, if the coefficient of kinetic friction between the trolley and the surface is 0.04? (Take g = 10 $\mathrm{m}/{\mathrm{s}}^2$). Neglect the mass of the string.

2.  9.6 $\mathrm{m}/{\mathrm{s}}^2$ and 2.71 N

3.  0.96 $\mathrm{m}/{\mathrm{s}}^2$ and 27.1 N

4.  0.63 $\mathrm{m}/{\mathrm{s}}^2$ and 30 N

A cyclist speeding at 18 km/h on a level road takes a sharp circular turn of radius 3 m without reducing the speed. The co-efficient of static friction between the tyres and the road is 0.1. Will the cyclist slip while taking the turn?

2.  Yes

3.  Data insufficient

4.  Depends on the weight of the cyclist

A circular racetrack of radius 300 m is banked at an angle of 15°. If the coefficient of friction between the wheels of a race-car and the road is 0.2, what is the (a) optimum speed of the race-car to avoid wear and tear on its tyres, and (b) maximum permissible speed to avoid slipping?

1.  ${\mathrm{v}}_{\mathrm{o}} = 28.1 \mathrm{m}/\mathrm{s} \mathrm{and} {\mathrm{v}}_{\max } = 38.1 \mathrm{m}/\mathrm{s}$

2.  ${\mathrm{v}}_{\mathrm{o}} = 38.1 \mathrm{m}/\mathrm{s} \mathrm{and} {\mathrm{v}}_{\max } = 28.1 \mathrm{m}/\mathrm{s}$

3.  ${\mathrm{v}}_{\mathrm{o}} = 0 \mathrm{m}/\mathrm{s} \mathrm{and} {\mathrm{v}}_{\max } = 28.1 \mathrm{m}/\mathrm{s}$

4.  ${\mathrm{v}}_{\mathrm{o}} = 38.1 \mathrm{m}/\mathrm{s} \mathrm{and} {\mathrm{v}}_{\max } = 100 \mathrm{m}/\mathrm{s}$

In the figure given below, a wooden block of mass 2 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on top of the block, the floor yields steadily and the block and the cylinder together go down with an acceleration of 0.1 $\mathrm{m}/{\mathrm{s}}^2$. What is the force of the block on the floor after the floor yields?
(Take g = 10 $\mathrm{m}/{\mathrm{s}}^2$.)
     
1. 270 N upward
2. 267.3 N downward
3. 20 N downward
4. 267.3 N upward