Grade 12Mechanics

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.

rajan jha

15 Years agoGrade 12

1 Answer

vikas askiitian expert

Approved Tutor Answer15 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/I_s)/(1 + mR²/I_d)

I_d = mR²/2 & I_s = 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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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.

rajan jha

1 Answer

vikas askiitian expert

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