Two bodies of m asses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string, a horizontal force F = 600 N is applied to (i) A, (ii) B along the direction of string. What is the tension in the string in each case ?

Explanation

(i) condition when force is applied on object B

Let tension in string = T
For motion of A
for motion of B
`(m_(2))/(m_(1)) = (F-T)/( T ) = (F)/( T ) = (T )/( T ) - (F )/( T )-1`
`:. , (30)/( 10) = (600)/( T )`
(ii) When force is applied on lignter object `(m_(1))`

Motion of A
`m_(1) a = F - T`
`m_(2) a = T`
By taking ratio of (2) and (1)
`(m_(1))/(m_(2)) = (F -T)/(T ) = (F )/( T^(2)) - 1`
`:. (30)/(20) = (600)/( T)`
`:. T = 400 N`