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Question:

When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60° with horizontal, it can travel a distance x1 along the plane. But when the inclination is decreased to 30° and the same object is shot with the same velocity, it can travel x2 distance. Then x1:x2 will be :

1:2

1:3

1:√3

2:1

Solution:

Correct option is C. 1:√3
(Stopping distance) x1 = u²/(2g sin60°)
(Stopping distance) x2 = u²/(2g sin30°)
=> x1/x2 = sin30°/sin60° = (1/2)/(√3/2) = 1:√3