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A disc and a solid sphere of same mass and radius roll do an inclined plane.The ratio of the friction force on the disc and sphere is a)7/6 b)5/4 c)3//2 d)depend on angle of inclination.

A disc and a solid sphere of same mass and radius roll do an inclined plane.The ratio of the friction force on the disc and sphere is 


a)7/6 b)5/4 c)3//2 d)depend on angle of inclination.

Grade:12

1 Answers

vikas askiitian expert
509 Points
12 years ago

for translational motion

mgsin@ - f = ma       ..........1         (f is friction is in backward direction)

for rotational motion

 fR = I(alfa)     ...........2

for pure rolling 

 a = (alfa)R

now eq 2 becomes

f = Ia/R2  .............3

from 1 & 3

 f(1 + mR2/I) = mgsin@

 f = mgsin@/(1+mR2/I)

friction on disc /friction on sphere = (1 + mR2/Is)/(1 + mR2/Id)

Id = mR2/2 & Is = 2mR2/5 are moment of inertia of disc & sphere respectively...

   ratio = (1+5/2)/(1+2)

          =7/6

option a) is correct

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