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Q.

A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an  angle 60° with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is 2−3/10s , then the height of the top of the inclined plane, in meters, is  ____________.Take g=10m/s2.

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answer is 0.75.

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Detailed Solution

ac=gsin⁡θ1+ICMR2 aring =gsin⁡θ2,adisc =2gsin⁡θ3 For ring hsin⁡θ=12gsin⁡θ2t12⇒t1=4hgsin2⁡θ=16h3g For disc, hsin⁡θ=122gsin⁡θ3t22⇒t2=3hgsin2⁡θ=4hg Given :t2−t1=16h3g−4hg=2−310⇒h43−2=2−3⇒h=(2−3)3(4−23)=32⇒h=0.75m
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A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an  angle 60° with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is 2−3/10s , then the height of the top of the inclined plane, in meters, is  ____________.Take g=10m/s2.