Figure shown two pulley arrangments for lifting a mass `m` . In case-1, the mass is lifting by attaching a mass 2m while in case-2 the mass is lifted by pulling the other end with a downward force `F=2mg` . If `a_(a)` and `a_(b)` are the accelerations of the two masses then (Assumme string is massless and pulley is ideal).

Options

A. `a_(a)=a_(b)`
B. `a_(a)=a_(b)/(2)`
C. `a_(a)=a_(b)/(3)`
D. `a_(a)=2a_(b)`

Answer

C

Explanation

In case-1, the acceleration of the system
`a_(a)=((2m-m)/(2m+m))g=(g)/(3)`
In case-2, the acceleration of the system
`a_(a)=((2m-m)/(2m+m))g=(g)/(3)=g`
So, `a_(a)=a_(b)//3` .