1) What should be the minimum force P to be applied to the string so that block of mass m just begins to move up the frictionless plane.

2) Both the blocks shown here are of mass m and are moving with constant velocity in direction shown in a resistive medium which exerts equal constant force on both blocks in direction opposite to the velocity.

The tension in the string connecting both of them will be : (Neglect friction)

(A) mg (B) mg/2

(C) mg/3 (D) mg/4

3) In which of the following cases is the contact force between A and B maximum (mA = mB = 1 kg)

4) A rope of mass 5 kg is moving vertically in vertical position with an upwards force of 100 N acting at the upper end and a downwards force of 70 N acting at the lower end. The tension at midpoint of the rope is

(A)100N (B) 125N (C) 85N (D)75N

5) Find the acceleration of 3 kg mass when acceleration of 2
kg mass is 2 ms–2_{ as shown in figure.}

(A) 3 ms–2 _{ (B) 2 ms}–2 _{(C) 0.5 ms}–2
(D) zero

6) A ball connected with string is released at an angle 45° with the vertical as shown in figure. Then the acceleration of the box at this instant will be: [Mass of the box is equal to mass of ball]

### (A) g/4

### (B) g/3

### (C) g/2

### (D) None of these

7) A ball of mass m is thrown vertically upwards. Assume the force of air

resistance has magnitude proportional to the velocity, and direction opposite to the velocity's. At the highest point, the ball's acceleration is

(A) 0 (B) less than g (C) g (D) greater than g

8) Two identical mass m are connected to a massless string which is hung over two frictionless pulleys as shown in figure. If everything is at rest, what is the tension in the cord?

(A) less than mg (B) exactly mg

(C) more than mg but less than 2mg (D) exactly 2mg

9) When F = 2N, the frictional force between 5 kg block and ground is

(A) 2N (B) 0 (C) 8 N (D) 10 N

10) When F = 2N, the frictional force between 10 kg block and 5 kg block is

(A) 2N (B) 15 N (C) 10 N (D) None

11)The maximum "F" which will not cause motion of any of the blocks.

(A) 10 N (B) 15 N (C) data insufficient (D) None

12) A ship of mass 3 x 107_{ kg initially at rest is pulled by a force of 5 x 10}4_{ N }
through a distance of 3 m. Assume that the resistance due to water is negligible,
the speed of the

ship is :

(a) 1.5 m/s (b) 60 m/s (c) 0.1 m/s (d) 5 m/s

13) A young man of mass 60 kg stands on the floor of a lift which is accelerating
downwards at 1 m/s2_{ then the reaction of the floor of the lift on the man is: (Take }
g = 9.8 m/s2)

(a) 528 N (b) 540 N 5" (c) 546 N (d) none of these

14) A block of mass 2 kg is placed on the floor. The coefficient of static friction is
0.4. If a force of 2.8 N is applied on the block parallel to floor, the force of friction
between the block and floor is (take g = 10 m/s2_{): }

(a) 2.8 N (b) 8 N (c) 2 N (d) none of these

15) In the figure, the blocks A, B and C each of mass m have accelerations a1, a2

and a3 respectively. F1 and F2 are external forces of

magnitude 2 mg and mg respectively.

16) A body of mass 2 kg is placed on rough horizontal plane. The coefficient of friction between body and plane is 0.2. Then:

(a) body will move in forward direction if F = 5 N

(b) body will be move in backward direction acceleration 0.5 m/s2_{ if}

force F = 3 N

(c) If F = 3 N then body will be in rest condition (d) both (a) and (c) are correct

17) Two blocks of masses M = 3 kg and m = 2 kg are in contact on a horizontal table. A constant horizontal force F = 5 N is applied to block M as shown. There is a constant frictional force of 2 N between the table and the block m but no frictional force between the table and the first block M, then acceleration of the two blocks is :

(a) 0.4 ms-2 _{(b) 0.6 ms}-2 _{(c) 0.8 ms}-2 _{ (d) 1 ms}-2

18) The coefficient of static friction between the bodies A and B is 0.30. Determine minimum stopping distance that the body A can have a speed of 70 km/h and B constant deceleration, if the body B is / not to

slip forward, is

19) The coefficient of static friction between the two blocks is 0.363, what is the minimum acceleration of block 1 so that block 2 does not fall ?

30º 2g R

5ms-1

FR

20) A block of mass 2 kg slides along a horizontal tabletop. A horizontal applied force of 12 N and a vertical applied force of 15 N act on the

block, as shown above. If the coefficient of kinetic friction between the block and the table is 0.2, the frictional force exerted on the block is most nearly

(A) 1 N (B) 3 N (C) 4 N (D) 5 N

(E) 7 N

1) A ball of mass 2kg is projected up a line of greatest slope inclined at an angle
of 30º to the horizontal. The coefficient of friction between the plane and the
ball is 0.4. The initial speed of the ball is 5 ms-1_{. Find:}

a) the frictional force acting whilst the ball moves up the plane.

b) the distance moved up the plane by the ball before it comes to instantaneous rest.

2) The AA man is towing a car along a straight horizontal road. The truck has a mass of 1500kg and the car has a mass of 850kg. The truck is connected to the car by a bar which is to be modelled as a light inextensible string. The truck’s engine produces a constant driving force of 2500N. The resistance to motion of the truck and the car are constant and of magnitude 750N and 400N respectively. Find:

a) the acceleration of the truck and the car b) the tension in the rope

When the truck and the car are traveling at 22ms-1

the tow bar breaks. If the magnitude of the resistance to motion of the truck remains at 750N calculate:

c) the time difference in achieving a speed of 30ms-1_{ with and without the car in}
tow

3) Two particles P and Q are connected by a light inextensible string which passes over a smooth fixed pulley. The system is released from rest. Find:

a) The magnitude of the acceleration b) Find the tension in the string.

R P B x T T F 6g 30º A 16g

4) Two particles P and Q of masses have masses 8m and Km, where K > 8. They are connected by a light inextensible string which passes over a smooth fixed pulley. The system is released from rest with the string taut and the hanging parts of the string vertical, as shown below. Initially P has an acceleration of magnitude of 3g/4

5) A particle A, of mass 0.9kg, rests on smooth horizontal table and is attached to one end of a light inextensible string. The string passes over a smooth pulley P fixed at the edge of the table. The other end of the string is attached to a particle B of mass 1.8kg which hangs freely below the pulley. The system is released from rest with the string taut and B at a height of 3.2m above the ground. In the subsequent motion A does not reach the pulley before B reaches the ground. Find:

a) the tension in the string before B reaches the ground. b) the time taken by B to reach the ground.

To make the model more realistic assume that the coefficient of friction between the particle and the table is 0.3.

Using the above modification find the time taken by B to reach the ground.

6) A particle, A of mass 6kg, rests on a rough plane inclined at an angle of 30º to the horizontal. The particle is attached to one end of a light inextensible string which lies in a line of greatest slope of the plane

and passes over a light smooth pulley P fixed at the top of the plane. The other end of the string is attached to a particle B of mass 16kg. The particles are released from rest with the string taut. The particle B moves down with an acceleration of 2g/5

7) A particle of mass 0.8kg rests on rough horizontal table and is attached to one end of a light inextensible string. The string passes over a smooth pulley P fixed at the edge of the table. The other end of the string is attached to a particle P of mass 1.4kg which hangs freely below the pulley. The coefficient of friction

A P B 1.2m 1.4g 0.8g R T T

between the particle and the table is 0.45. The system is released from rest with the string taut and B at a height of 1.2m above the

ground. At the point of release A is 1.8m from P. Find: a) the acceleration of the particles.

b) the time taken by B to reach the ground. c) the speed with which A hits P.