STATEMENT-1In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.becauseSTATEMENT-2In an elastic collision, the linear momentum of the system is conserveda)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Statement-1: In an elastic collision between two bodies, the relative speed of the bodies after the collision is equal to the relative speed before the collision.

Statement-2: In an elastic collision, the linear momentum of the system is conserved.

Explanation:

To determine the correctness of the given statements, let's understand the concept of elastic collision and linear momentum conservation.

Elastic Collision:
An elastic collision is a type of collision in which both kinetic energy and linear momentum are conserved. This means that the total kinetic energy and total linear momentum of the system before the collision are equal to the total kinetic energy and total linear momentum of the system after the collision.

Linear Momentum:
Linear momentum is the product of an object's mass and its velocity. It is a vector quantity and is conserved in a closed system where no external forces are acting.

Explanation of Statement-2:
In an elastic collision, the linear momentum of the system is conserved. This means that the total linear momentum of the system before the collision is equal to the total linear momentum of the system after the collision. Mathematically, it can be represented as:

m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

where m1 and m2 are the masses of the bodies, u1 and u2 are their initial velocities, and v1 and v2 are their final velocities.

Explanation of Statement-1:
In an elastic collision, the relative speed of the bodies after the collision is equal to the relative speed before the collision.

To understand why this is true, let's consider an example. Suppose two objects A and B are moving towards each other with velocities u1 and u2 respectively. After the collision, object A moves in the opposite direction with final velocity v1, and object B moves in the opposite direction with final velocity v2. The relative speed of the bodies before the collision is given by:

Relative Speed before collision = |u1 - u2|

Similarly, the relative speed of the bodies after the collision is given by:

Relative Speed after collision = |v1 - v2|

Since the linear momentum is conserved in an elastic collision, we can equate the initial and final linear momenta:

m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

From this equation, we can deduce that the relative speed of the bodies after the collision is equal to the relative speed before the collision:

|v1 - v2| = |u1 - u2|

Therefore, Statement-1 is true.

Explanation of Statement-2 as an explanation for Statement-1:
Statement-2, which states that the linear momentum of the system is conserved in an elastic collision, provides a valid explanation for Statement-1. The conservation of linear momentum ensures that the relative speed of the bodies after the collision is equal to the relative speed before the collision. Hence, Statement-2 is a correct explanation for Statement-1.

Therefore, the correct answer is option 'B' - Statement-1 is true, Statement-2 is true, and Statement-2 is a correct explanation for Statement-1.

Answer

In Collisions:

1. Momentum is conserved both in elastic and inelastic collisions.

2. Kinetic Energy is also conserved in elastic collisions.

Point 1 leads to Statement 2, i.e, 'In an elastic collision, the linear momentum of the system is conserved.

Point 2 leads to Statement 1, i.e, 'In an Elastic Collision between 2 bodies, the relative speed of the bodies after the collision is equal to the relative speed before the collision'.

Thus, both Statement 1 and Statement 2 are true, but Statement 2 is not the reason for Statement 1.

Similar Class 11 Doubts

Statement I : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.Statement II : Principle of conservation of momentum holds true for all kinds of collisions. [AIEEE 2010]

Statement-I : A point particle of mass m moving with speed u collides with stationary point particle of mass M. If the maximum energy loss possible is given asthen f =.Statement-II : Maximum energy loss occurs when the particles get stuck together as a result of the collision. [JEE MAIN 2013]

Statement-1: At Boyles temperature a real gas behaves as ideal gas for wide range of temperature and pressure.Statement-2: At Boyles temperature vanderwaal constant a and b compensate each other.

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