Laws of Motion

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