An object is shot from the bottom of a long smooth inclined plane with speed u. When the plane is at 60° to the horizontal it travels a distance x₁ before stopping. When the plane is at 30° and the same object is shot with the same speed, it travels x₂. Then x₁: x₂ is:
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Question

An object is shot from the bottom of a long smooth inclined plane with speed u. When the plane is at 60° to the horizontal it travels a distance x₁ before stopping. When the plane is at 30° and the same object is shot with the same speed, it travels x₂. Then x₁: x₂ is:

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G1 Physics · Accepted Answer

Step 1: Along a smooth incline the retardation is g sinθ. Step 2: Using 0=u²−2(g sinθ)x gives x=u²/[2g sinθ]. Step 3: Thus x₁/x₂ = sin30°/sin60° = (1/2)/(√3/2)=1/√3. Therefore x₁:x₂=1:√3. Final answer: B.

An object is shot from the bottom of a long smooth inclined plane with speed u. When the plane is at 60° to the horizontal it travels a distance x₁ before stopping. When the plane is at 30° and the same object is shot with the same speed, it travels x₂. Then x₁:x₂ is: