Question

a. Law of conservation of Linear Momentum and its application with reference to Recoil of a Gun​

Answer 1

LAW OF CONSERVATION.

Explanation:

By the principle of conservation of linear momentum, total linear momentum before firing is equal to the total momentum after firing. Negative sign shows that direction of is opposite to that of , i.e., gun recoils as m2 is much greater than m1. i.e., heavier gun will recoil with smaller velocity.

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Answer 2

Answer:

Law of conservation of linear momentum and its applications

It states that the total momentum of an isolated system of interacting particles is conserved. Suppose an isolated system consisting of n particles of masses m1, m2, ...... mn moving with velocities

respectively.

The vector sum of linear momenta, i.e., total linear momentum of all bodies in the system is given by

Let m be the total mass of the system and be the velocity of the centre of mass of the system

Therefore,

Differentiating above equation w. r. t. time, we get,

where is acceleration of centre of mass of the system.

By Newton’s Second Law of Motion

(external force)

In case of isolated system, no external force is acting on the system, i.e.,

The above equation justifies the principle of conservation of linear momentum.

Recoiling of a gun

When the bullet is fired from a gun, the gun recoils. The recoil velocity of the gun can be calculated from the principle of conservation of linear momentum. Let m1 = mass of bullet, = velocity of bullet, m2 = mass of gun and = velocity of recoil of the gun. Before firing, the gun and the bullet both are at rest. Therefore, total momentum before firing = 0. Therefore, vector sum of linear momentum after firing = m1 + m2. By the principle of conservation of linear momentum, total linear momentum before firing is equal to the total momentum after firing.

Negative sign shows that direction of is opposite to that of , i.e., gun recoils as m2 is much greater than m1.

Therefore, is much less than

i.e., heavier gun will recoil with smaller velocity.