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Q.

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Two identical solid discs are released from the top of two inclined surfaces having same height h and angle of inclination θ with horizontal. One inclined surface is perfectly smooth and the other one is rough enough to allow the disc to roll without slipping. When the discs arrive at the bottom of respective inclined surfaces, Then kinetic energies of spheres are Ks(smooth) and Kr (rough). Then Ks:Kr is 

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a

3 : 2

b

3 : 4

c

1 : 3

d

4 : 3

answer is A.

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Detailed Solution

Conserving energy, Ks=mgh ------(1)

and Kr+1212mr2vr2=mgh

 Kr+12Kr=mghKr=23mgh -----(2)

Ks:Kr=mgh:23mgh=3 : 2

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