Question

How to do 164th question?

Answer 1

30 N

I have taken `g=10 " ms"^-2` throughout.

Explanation:

As long as the tension in the string does not exceed 500 N , the block on the left will not move. We will assume that this is the case and begin the analysis.

In this situation, if the rightmost weight descends a distance `x`, then the block in the middle must rise by a distance `x/2`. Thus, if the acceleration of the former is `a` downwards, that of the latter is `a/2` upwards.

We now write down the equation of motion for the two blocks (assuming the tension to be `T` N)

`50 - T = 5a,qquad 2T-50 = 5a/2 implies`

`50 -T = (2T-50)times 2 = 4T-100 implies`

`5T = 150 implies T=30`

Since this works out to be less than 500 N, our initial assumption about the block on the left not moving is justified.