The pulleys in figure are identical, each having a radius R and moment of inertia I. Find the acceleration of the block M.

Answer

B

Explanation

According to the equation
`Mg-T_1=Ma`….1

`(T_1-T_2)R=I a/R`
`rarr (T_1-T_2)=I a/R^2`….. 2
`rarr (T_2-T_3)R=I a/R^2`……3
`rarr T_3-mg=ma`…..4
By adding equation 2 and 3 we will get
`rarr (T_1-T_3)=(2Ia)/R^2`......5
By adding equation 1 and 4 we will get ltbr. `-mg+Mg+(T_3-T_1)=Ma+ma..6 `
Substitung the value of `T_3-T_1` we will get
`rarr Mg-mg=Ma+ma+(2Ia)/R^2`
`rarr a=((M-m)G)/((M+m+2I/R^2)0`