A unifrom horizontal `200 N` beam `AB` length `L` has two weights hanging from it, `300 N` at `L//3` from end `A` and `400 N` at `3L//4` from the same end. What single additional force acting on the beam will produced equilibrium ?

Options

A. `900 N`, in the middle
B. `900 N`, at `0.4 L` from `A`
C. `900 N, at 0.46 L` from `A`
D. `900 N`, at `0.56 L` from `A`

Answer

D

Explanation

(d) The magnitude of single force should be
`200 + 300 + 400 = 900 N`
`Sigma tau_A = 0`
`rArr 300 xx (L)/(3)+200 xx (L)/(2) = 400 xx (3 L)/(4) = 900 x`
`rArr x = (5)/(9) L = 0.555 L ~~ 0.56 L`.
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