Two identical uniform discs of mass `m` and radius `r` are arranged as shown in the figure. If `alpha` is the angular acceleration of the lower disc and `a_(cm)` is acceleration of centre of mass of the lower disc, then relation among `a_(cm), alpha` and `r` is

Options

A. `a_(cm)=alpha/r`
B. `a_(cm)=2alphar`
C. `a_(cm)=alphar`
D. none of these

Answer

B

Explanation

`T_(r)=(mr^(2))/2alpha_(1)`………….i
`T_(r)=(mr^(2))/2alpha`………….ii
`alpha_(1)=alpha`…………………iii
From i and ii

Acceleration of point `b=` acceleration of point `a`
`ralpha_(1)=a_(cm)-ralpha`………..iv
Here `2raA:=a_(cm)`