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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.
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
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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