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Grade 11General Physics

Two uniform solid spheres of the same size, but different mass, are released from rest simultaneously at the same height on a hill and roll to the bottom without slipping. which will reach first?

Profile image of riya
10 Years agoGrade 11
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1 Answer

Profile image of Riddhish Bhalodia
ApprovedApproved Tutor Answer10 Years ago

consider a sphere with moment of inertia as
I = \beta MR^2 ,\beta being a scalar constant

Now as it’s ideal rolling at any height h from the top of the hill if we apply energy conservation we have the following
0.5Mv^2 + 0.5\beta MR^2 \omega^2 = Mgh
the M cancels out and hence at any point on the hilll the velocity of the object is independent of mass
so it the time to reach bottom
Hence both will reach bottom at the same time