Laws of Motion

A box of mass 15 kg is kept on the floor of a stationary trolley. The coefficient of static friction between the box and the trolley is 0.12. Keeping the box in stationary state over the trolley, the maximum acceleration with which the trolley can be moved horizontally in m s-2 is : (g = 10 m/s2)

1. 1.8
2. 1.2
3. 1.5
4. 2.1

The magnitude and direction of the acceleration produced in a body of mass 5 kg when two mutually perpendicular forces 8 N and 6 N act on it, are respectively :

1. 2 m s-2; -1(3/4) with 8 N force
2. 2 m s-2; -1(4/3) with 8 N force
3. 2 m s-2; -1(3/4) with 6 N force
4. 20 m s-2; -1(4/3) with 8 N force

A car travels on a circular racetrack of radius 50 m, which is banked at an angle . If the car travels at a speed 10 ms-1, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be 10 ms-2, the value of is:

1. -1(2 3)
2. -1 ( 15 )
3. -1 ( 25 )
4. -1( 3/2)

A frictionless circular wire of unit radius is fixed on the horizontal plane. Two-point particles of unit mass start moving simultaneously from point A ( = 2 ) with identical uniform angular speeds in opposite directions, and meet again at point B ( = - 2 ). During this time, which of the following figures schematically represent the magnitude of the total linear momentum P of the system, as a function of ? [figure]

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A ball of mass 0.5 kg is dropped from a height of 40 m. The ball hits the ground and rises to a height of 10 m. The impulse imparted to the ball during its collision with the ground is (Take g = 9.8 m/s2)

1. 0
2. 84 N s
3. 21 N s
4. 7 N s

There are two inclined surfaces of equal length (L) and same angle of inclination 45 with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction ( k) between the object and the rough surface is close to

1. 0.5
2. 0.75
3. 0.25
4. 0.40

A horizontal force 10 N is applied to a block A as shown in figure. The mass of blocks A and B are 2 kg and 3 kg respectively. The blocks slide over a frictionless surface. The force exerted by block A on block B is : [figure]

1. Zero
2. 4 N
3. 6 N
4. 10 N

A bob is whirled in a horizontal plane by means of a string with an initial speed of rpm. The tension in the string is T. If speed becomes 2 while keeping the same radius, the tension in the string becomes:

1. T
2. 4T
3. T4
4. 2T

A bob is whirled in a horizontal circle by means of a string at an initial speed of 10 rpm. If the tension in the string is quadrupled while keeping the radius constant, the new speed is:

1. 20 rpm
2. 40 rpm
3. 5 rpm
4. 10 rpm

A box of mass 5 kg is pulled by a cord, up along a frictionless plane inclined at 30 with the horizontal. The tension in the cord is 30 N. The acceleration of the box is (Take g = 10 m s-2)

1. 2 m s-2
2. Zero
3. 0.1 m s-2
4. 1 m s-2

A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is :

1. along northward
2. along north-east
3. along south-west
4. along eastward

Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 (g = 10 m s-2 ).

1. 150 m s-2
2. 1.5 m s-2
3. 50 m s-2
4. 1.2 m s-2

A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2 : 2 : 1. If the fragments having equal mass fly off along mutually perpendicular directions with speed v, the speed of the third (lighter) fragment is :

1. v
2. 2v
3. 2 2v
4. 3 2v

The distance covered by a body of mass 5 g having linear momentum 0.3 kg m/s in 5 s is :

1. 0.3 m
2. 300 m
3. 30 m
4. 3 m

In the diagram shown, the normal reaction force between 2 kg and 1 kg is (Consider the surface, to be smooth) : (Given g = 10 m s-2) [figure]

1. 10 N
2. 25 N
3. 39 N
4. 6 N

A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is (g = 10 m/s2) nearly :

1. 1.4 kg m/s
2. 0 kg m/s
3. 4.2 kg m/s
4. 2.1 kg m/s

Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is : [figure]

1. g/2
2. g/5
3. g/10
4. g

A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be : (g = 10 m/s2)

1. 102 rad/s
2. 10 rad/s
3. 10 rad/s
4. 10 rad/s

A particle moving with velocity V is acted by three forces shown by the vector triangle PQR. The velocity of the particle will : [figure]

1. remain constant
2. increase
3. decrease
4. change according to the smallest force QR

Which one of the following statements is incorrect?

1. Rolling friction is smaller than sliding friction.
2. Limiting value of static friction is directly proportional to normal reaction.
3. Frictional force opposes the relative motion.
4. Coefficient of sliding friction has dimensions of length.

A block of mass m is placed on a smooth inclined wedge ABC of inclination as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and for the block to remain stationary on the wedge is [figure]

1. a = gcosec
2. a = g
3. a = g
4. a = g

One end of string of length l is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed 'v', the net force on the particle (directed towards centre) will be (T represents the tension in the string)

1. T + mv2l
2. T - mv2l
3. zero
4. T

Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively [figure]

1. g3, g
2. g, g
3. g3, g3
4. g, g3

A car is negotiating a curved road of radius R. The road is banked at an angle . The coefficient of friction between the tyres of the car and the road is s. The maximum safe velocity on this road is

1. gR s + 1 - s
2. gR2 s + 1 - s
3. gR2 s + 1 - s
4. gR s + 1 - s

A rigid ball of mass m strikes a rigid wall at 60 and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be : [figure]

1. mV
2. 2 mV
3. mV2
4. mV3

A bullet of mass 10 g moving horizontally with a velocity of 400 m s-1 strikes a wood block of mass 2 kg which is suspended by light inextensible string of length 5 m. As a result, the centre of gravity of the block is found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be

1. 100 m s-1
2. 80 m s-1
3. 120 m s-1
4. 160 m s-1

Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius r2 and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is

1. 4
2. 1
3. 2
4. 3

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30 , the box starts to slip and slides 4.0 m down the plank in 4.0 s. [figure] The coefficients of static and kinetic friction between the box and the plank will be, respectively

1. 0.5 and 0.6
2. 0.4 and 0.3
3. 0.6 and 0.6
4. 0.6 and 0.5

A block A of mass m1 rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m2 is suspended. The coefficient of kinetic friction between the block and the table is k. When the block A is sliding on the table, the tension in the string is

1. m1m2(1+ k)g(m1+m2)
2. m1m2(1- k)g(m1+m2)
3. (m2+ km1)g(m1+m2)
4. (m2- km1)g(m1+m2)

Three blocks A, B and C, of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is [figure]

1. 8 N
2. 18 N
3. 2 N
4. 6 N