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

C

Explanation

(c ) `(x_(P)-x_(1))+(x_(P)-x_(2))`=length of string= constant
Differentiating twice with respect to time, we get

`a_(P)=(a_(1)+a_(2))/(2)`
Here `a_(P)=A,a_(1)` is positive and `a_(2)` is negative. Hence,
`A=(a_(1)-a_(2))/(2)`