Find the tension in the string in situation as shown in the figure below . Forces 120 N and 100N start acting when the system is at rest.

Explanation

(i) Let us assume that system moves towards left then as it is clear from FBD, net force in horizontal direction is towards right. Therefore the assumption is not valid.

Above assumption is not possible as net force on system comes towards right. Hence system is not moving towards left.
(ii) Similarly let us assume that system moves towards right.

Above assumption is also not possible as net force on the system is towards left in this situation. Hence assumption is again not valid.
Therefore it can be concluded that the system is stationary

Assuming that the 10 kg block reaches limiting friction first then using FBD’s

`120=T+90 rArr T=30N`
Also `T+f=100``
`therefore 30+f=100 rArr f=70N`
which is not possible as the limiting value is 60 N for this surface of block.
`therefore` Our assumption is wrong and now taking the 20 kg surface to be limiting we have

`T+60=100N rArr T=40N`
Also `f+T=120N rArr f=80N`
This is acceptable as static friction at this surface should be less than 90 N.
Hence the tension in the string isT = 40 N