Question

Directions: Some questions (Assertion – reason type) are given below. Each question contains Statement I (Assertion) and statement II (Reason). Each question has 4 choices (a), (b), (c) and (d) out of which only one is correct. So, select the correct choice.

Statement I A single particle is having non- zero kinetic energy then its momentum can be zero.

Statement II Kinetic energy is a scalar quantity and is always positive, while momentum is a vector quantity.

• A. Statement I is true, statement II is true, statement II is a correct explanation for statement I
• B. Statement I is true, statement II is true, statement II is not a correct explanation for statement I
• C. Statement I is true, statement II is false
• D. Statement I is false, statement II is true

Answer 1

The correct option is D

Statement I is false, statement II is true

Assertion:

1. For a single particle, if it has zero momentum then kinetic energy will be zero. $K=\frac{p^2}{2m}$
2. Hence particles with non-zero kinetic energy have non-zero momentum.

Statement I is false.

Reason:

1. Kinetic energy $K=\frac{1}{2}m{v}^2$ is a scalar quantity. Since mass and $v^2$ are always positive, kinetic energy is positive.
2. Momentum $\overrightarrow{P}=m\overrightarrow{v}$ is a vector quantity and it will be in the direction of velocity.

Statement II is true.

Therefore, the assertion is false but the reason is true.

Hence, option (d) is the correct answer