Two pulley arrangements (A) and (B) are as shown in the figure. Neglect the masses of the ropes and pulleys and the friction at the axle of the pulleys. The ratio of the acceleration of mass m in arrangement (A) to that in arrangement (B) is

Options

A. `1:1`
B. `1:2`
C. `1:3`
D. `2:1`

Answer

C

Explanation

in case A accelertion of mass m is
`a=((2m-m)g)/(m+2m) =(g)/(3)`
in case B, the acceleration of mass m is
` a. = (2 mg - mg )/(m ) =g therefore (a)/(a.) = (1)/(3)`