A uniform solid sphere rolls without slipping from rest through the same vertical height on inclines of 30° and 45°, attaining speeds v₁ and v₂ respectively. The ratio v₁²/v₂² is:
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A uniform solid sphere rolls without slipping from rest through the same vertical height on inclines of 30° and 45°, attaining speeds v₁ and v₂ respectively. The ratio v₁²/v₂² is:

G1 Physics · Accepted Answer

By conservation of mechanical energy, mgh=½mv²+½Iω². For the same body and same vertical drop h, final speed is independent of incline angle. Hence v₁=v₂ and v₁²/v₂²=1.