In the arrangement of three block as shown in fig. the string is inextensible. If the direction of accelerations are as shown in the figure, then determine the constraint relation.

Explanation

Let us assume respective distance of each block as shown in fig. since the length of the string is constant `x_(1)+x_(2)+2x_(3)=` constant.

On differentiating twice w.r.t . Time we get
`(d^(2)x_(1))/(dt)+(d^(2)x_(2))/(dt^(2))+2(d^(2)x_(3))/(dt^(2))=0`
Since `x_(1)` and `x_(2)` are assumed to be decreasing with time,
`(d^(2)x_(1))/(dt^(2))=-a_(1)` and `(d^(2)x_(2))/(dt^(2))= -a_(2)`
and `x_(3)` is assumed to be increasing with time. therefore,
`(d^(2)x_(3))/(dt^(2))= +a_(3)`
thus, `-a_(1)-a_(2)+2a_(3)=0` or `a_(1)+a_(2)=2a_(3)`.