STATEMENT-1
For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.
and
STATEMENT-2
If the observer and the object are moving at velocities and respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is .
For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.
and
STATEMENT-2
If the observer and the object are moving at velocities and respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is .
- (A)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
- (B)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1✓ Correct
- (C)STATEMENT-1 is True, STATEMENT-2 is False
- (D)STATEMENT-1 is False, STATEMENT-2 is True
Answer: (B)
Solution
STATEMENT-1 is true: Nearby objects appear to move backward relative to the train due to parallax effect, while distant objects appear stationary because the angle they subtend changes very slowly.
STATEMENT-2 is true: The relative velocity formula is correct.
However, STATEMENT-2 does not explain STATEMENT-1. The phenomenon described in STATEMENT-1 is due to the angular displacement (parallax) being inversely proportional to distance, not just relative velocity. Distant objects subtend very small angles at the observer's eye, so their apparent motion is negligible.
STATEMENT-2 is true: The relative velocity formula is correct.
However, STATEMENT-2 does not explain STATEMENT-1. The phenomenon described in STATEMENT-1 is due to the angular displacement (parallax) being inversely proportional to distance, not just relative velocity. Distant objects subtend very small angles at the observer's eye, so their apparent motion is negligible.
JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Single correct option