Assertion and Reason are given in following questions. Each...

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it. (1) If both assertion and reason and the reason is the correct explanation of the Assertion. (2) If both assertion and reason are true but reason is not the correct explanation of the assertion. (3) If the assertion is true but reason is false. (4) If the assertion and reason both are false. Assertion : Two bodies of different masses have same momentum. Their kinetic energy are in the inverse ratio of their masses. Reason $: \mathrm{K} . \mathrm{E} .=(1 / 2) \mathrm{mv}^{2}$ (A) 1 (B) 2 (C) 3 (D) 4

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion : Two bodies of different masses have same momentum. Their kinetic energy are in the inverse ratio of their masses. Reason $: \mathrm{K} . \mathrm{E} .=(1 / 2) \mathrm{mv}^{2}$
(A) 1
(B) 2
(C) 3
(D) 4

Key Concepts

Momentum

Momentum is a vector quantity defined by the product of an object's mass and velocity. It represents the quantity of motion an object has and is conserved in isolated systems. Understanding momentum is crucial for analyzing collisions and interactions in mechanics.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = (1/2)mv². This scalar quantity is dependent on both the mass of the object and the square of its velocity, highlighting how changes in speed have a significant impact on the energy involved.

Relationship between Momentum and Kinetic Energy

When momentum is held constant, the kinetic energy of a moving object can be expressed in relation to its mass by substituting velocity from the momentum equation (v = p/m) into the kinetic energy formula. This leads to an expression where kinetic energy is inversely proportional to mass, emphasizing that for objects with the same momentum, a smaller mass corresponds to a higher kinetic energy.

Assertion and Reason Question Type

Assertion and Reason questions are designed to test both subject knowledge and the ability to logically connect statements. One must assess the truth of each statement independently and then determine whether the reason provided appropriately explains the assertion, which is a common format in physics and broader scientific assessments.

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