Question

A block ‘A’ of mass ${m_1}$ hits horizontally the rear side of a spring (ideal) attached to a block B of mass ${m_2}$ resting on a smooth horizontal surface. After hitting, ‘A’ gets attached to the spring.

Some statements are given at any moment of time:
i. If velocity of A is greater than B, then kinetic energy of the system will be decreasing.
ii. If velocity of A is greater than B, then kinetic energy of the system will be increasing.
iii. If velocity of A is greater than B, then momentum of the system will be decreasing.
iv. If velocity of A is greater than B, then momentum of the system will be increasing.

Now select correct alternative
A. Only iv
B. Only i
C. ii and iv
D. i and iii

Answer 1

Hint:
First let us see what kinetic energy and potential energy of a system is-
An object’s kinetic energy is the energy it possesses due to its motion. It is defined as the work required to accelerate from rest to the specified velocity of a body of a given mass.
$K.E = \dfrac{1} {2}m{v^2}$

Potential energy is the energy retained by an object regardless of its location pressures within itself, its electrical charge, or other variables relative to other objects.
The product of a system’s mass multiplied by its velocity is known as linear momentum.

Complete step by step solution:
Now let us see what law of conservation of momentum means-
The law of momentum states that the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision for a collision that happens between object 1 and object 2 in an independent structure. That is, the momentum that object 1 has lost is equal to the momentum that object 2 has acquired.
Given,
A block ‘A’ of mass ${m_1}$ hits horizontally the rear side of a spring (ideal) attached to a block B of mass ${m_2}$ resting on a smooth horizontal surface. After hitting, ‘A’ gets attached to the spring.
Statement i is right, since spring will be compressed in this situation. So, potential energy is going to increase here. It means that the system’s kinetic energy will reduce while the system’s overall mechanical energy is constant.

In comparison, the system’s momentum will be conserved. It will not increase nor will it decrease.
Correct alternative is B

Note:
Here we have to observe the question and see which block is attached to the spring first and whether the spring is attached horizontally or vertically. Springs are a special example of a system which, due to either compression or stretching, can store elastic potential energy. A force is needed to compress a spring; the further compression there is, the further force is needed to further compress it.