What are unbalanced forces? Give examples.

What is relationship between mass and inertia? Give the SI unit of mass and inertia.

State and explain Newton's second law of motion.

State the law of conservation of momentum. Prove this law by taking the case of collision of two bodies.
Hence in the absence of an external force, the total momentum of a group of objects remains unchanged or conserved during the collision. This is the law of conservation of momentum.

Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of \(2m{s}^{-1}\) and \(1m{s}^{-1}\), respectively. They collide and after the collision, the first object moves at a velocity of \(1.67 m s ^{-1}\) Determine the velocity of the second object.

A body of mass 2 kg, initially moving with a velocity of \(10 m {s}^{-1}\)collides with another body of mass 5 kg at rest. After collision velocity of ifrst bdy becomes \(1 m {s}^{-1}\) .Find the velocity of the second body.

Two objects, each of mass 1.5 kg, are moving in the same straight line but in opposite directions, The velocity of each object is \(2.5 m s^{-1}\) before the collision during which they stick together. What will be the velocity of the combined object after collision?

How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m s^–2.

A motorcar of mass 1,200 kg is moving along a straight line with velocity of 90 km/h. Its velocity is slowed down to 18 km.h s by an unbalanced external force. Calculate the acceleration and change in momentum. Also, calculate the magnitude of the force required.

The second law of motion is often seen in action in our everyday life. You must have noticed that while catching a fast moving cricket ball, a fielder in the ground gradually pulls his hands backwards with the moving ball. In doing so, the fielder increases the time during which the high velocity of the moving ball decreases to zero. Thus, the acceleration of the ball is also reduced. If the ball is stopped suddenly then its high velocity decreases to zero in a very short interval of time. Thus the rate of change of momentum of the ball will be large. Therefore, a large force would have to be applied for holding the catch that may hurt the palm of the fielder.
(a) State Newton second law of motion.
(b) State relation between force of momentum.
(c) What is the SI unit of force?
(d) Why we are hurt less when we jump on a muddy floor in comparison to a hard floor?