Two masses are connected by a string which passes over a pulley acceleration upward at a rate `A` shown. If `a_(1)` and `a_(2)` be the accelerations of bodies 1 and 2 respectively then,

Options

A. `A=(a_(1)+a_(2))`
B. `A=(a_(1)-a_(2))`
C. `A=(a_(1)+a_(2))/(2)`
D. `A=(a_(1)-a_(2))/(2)`

Answer

D

Explanation

Since length of the string is constant So,
`(Y_(P)-y_(1))+piR+(Y_(P)-y_(2))` =constant.
Take derivative of both sides twice w.r.t. time `t` ,
We get, `ddotY_(p)-ddoty_(1)+ddotY_(p)-ddoty_(2)=0`
implies `A=(a_(1)+a_(2))/(2)` .