A vertical bar of uniform section is fixed at both of its ends and a load $W = 5000 N$ is applied axially at an intermediate section as shown in figure.
Select the correct statements (s):

Reaction at the bottom support is

3000 N

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Reaction at the bottom support is

2000 N

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Reaction at the top support is

1000 N

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Reaction at the top support is

3000 N

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Solution

The correct options are
B Reaction at the bottom support is $2000 N$
D Reaction at the top support is $3000 N$
We know from the formula of young's modulus
$Y = \frac{F \times l}{A \times Δ l}$

$\Rightarrow F = \frac{Y \times A \times Δ l}{l}$
As both the ends are fixed $Δ l = 0$
So the net force acting will be zero
$F_{1} + F_{2} = 0$
And the force will be divided inversely to the value of length.
$\frac{F_{1}}{F_{2}} = \frac{l_{2}}{l_{1}} = \frac{2}{3}$

Solving these two equations we get, $F_{1} = 2000 N$ and $F_{2} = 3000 N$

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A vertical bar of uniform section is fixed at both of its ends and a load W=5000 N is applied axially at an intermediate section as shown in figure.Select the correct statements (s):

A vertical bar of uniform section is fixed at both of its ends and a load $W = 5000 N$ is applied axially at an intermediate section as shown in figure.
Select the correct statements (s):