Rotational problem- 10th Feb'15

Question

Let !!a_1!! and !!a_2!! be their linear accelerations then:

a) !!a_1 = a_2!!

b) !!a_1 > a_2!!

c) !!a_1 < a_2!!

d) Data insufficient

Solution

Taking torque about contact point,

!!F(2r)= (I_(CM)+ mr^2)alpha....(1)!!

and !!A_(CM)= r alpha.....(2)!!

From equation (1) and (2), we will get

!!=> (F(2r)r)/(I_(CM)+ mr^2) = A_(CM)!!

As !!I_(CM)!! is more, !!A_(CM)!! is less.

!!I_(CM1)!! for solid sphere, !!= 2/5 mr^2!!

!!I_(CM2)!! for hollow sphere, !!= 2/3 mr^2!!

We can see clearly that, !!I_(CM2) >I_(CM1)!!

Therefore, !!A_(CM2) < A_(CM1)!!

!!=> a_1> a_2!!

Therefore, option (b) is correct.