Blocks on a Smooth Inclined Plane – Rankers Physics
Topic: Laws of Motion
Subtopic: Linear Momentum and Second Law of Motion

Blocks on a Smooth Inclined Plane

Assertion (A): Two smooth blocks are kept on a smooth inclined plane such that one block is kept over other. When a force is applied on upper block acceleration of lower block is unaffected.
Reason (R): Acceleration of a block on smooth inclined plane is \(g sin(\theta)\).
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution:

Assertion (A) is true: Since both blocks are on smooth surfaces (implying no friction between blocks), a force applied *only* to the upper block will not be transmitted horizontally to the lower block. The upper block will slide over the lower. The lower block will continue to accelerate down the smooth inclined plane solely due to gravity.

Reason (R) is true: The acceleration of any block on a smooth inclined plane (where \(theta\) is the angle of inclination) is indeed \(g sin(theta)\), assuming no other forces. Reason (R) states a fact about acceleration on an inclined plane. While it describes the acceleration of the lower block, it does not explain *why* the force on the upper block has no effect on it (which is due to the lack of friction between them).

Therefore, (A) and (R) are true, but (R) is not the correct explanation of (A).

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