Laws of Motion

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

A balloon with mass m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration a?

1. 2mag+a
2. 2mag-a
3. mag+a
4. mag-a

A system consists of three masses m1, m2 and m3 connected by a string passing over a pulley P. The mass m1 hangs freely and m2 and m3 are on a rough horizontal table (the coefficient of friction = ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m1 is (Assume m1 = m2 = m3 = m) [figure]

1. g(1 - g )9
2. 2g 3
3. g(1 - 2 )3
4. g(1 - 2 )2

The force F acting on a particle of mass m is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is : [figure]

1. 24 N s
2. 20 N s
3. 12 N s
4. 6 N s

A body of mass (4m) is lying in x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is :

1. mv2
2. 32mv2
3. 2mv2
4. 4mv2

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 m s-1 and the second part of mass 2 kg moves with 8 m s-1 speed. If the third part flies off with 4 m s-1 speed, then its mass is :

1. 7 kg
2. 17 kg
3. 3 kg
4. 5 kg