In the figure shown the relation between acceleration is -

Options

A. `a_(1)+a_(2)+2a_(3)=0`
B. `a_(1)+a_(2)=2a_(3)`
C. `a_(1)+a_(2)=a_(3)`
D. `a_(1)+a_(2)+a_(3)=0`

Answer

B

Explanation

Let we consider displacement of `m_(1)` is `x_(1)` and displacement of `m_(2)` is `x_(2)` and vertical displacement of `m_(3)` is y
`y=(x_(1)+x_(2))/(2)`
2y=`x_(1)+x_(2)`
differentiate this `2(dy)/(dt)=(dx_(1))/(dt)+(dx_(2))/(dt)`
differentiate again `2(d^(2)y)/(dt^(2))=(dx_(1)^(2))/(dt)+(dx_(2)^(2))/(dt)`
`rArr 2a_(3)=a_(1)+a_(2)`