A steel ball is suspended from the ceiling of an acceleration carriage by means of two cords A and B. Determine the acceleration a of the carriage which will cause the tension in A to be twice that in B.

Explanation

`T_(1) cos 60^(@)-T_(2) cos 60^(@)=ma`
`T_(1) sin 60^(@) + T_(2) sin 60^(@)=mg`
`T_(1)=2T_(2)`
On solving equations we get
`T_(1)=(4mg)/(3sqrt(3)), T_(2)=(2mg)/(3 sqrt(3))`,
and `a=(g)/(3 sqrt(3))`.