MHT CET · Physics · Mechanical Properties of Solids

Let a steel bar of length 'l', breadth 'b' and depth 'd' be loaded at the centre by a load 'W'. Then the sag of bending of beam is (Y = Young's modulus of material of steel)

A $\frac{W l^{3}}{2 b d^{3} Y}$
B $\frac{W l^{3}}{4 b d^{3} Y}$
C $\frac{W l^{3}}{2 d b^{3} Y}$
D $\frac{W l^{3}}{4 d b^{3} Y}$

Verified Solution

Answer & Solution

Correct Answer

(B) $\frac{W l^{3}}{4 b d^{3} Y}$

Step-by-step Solution

Detailed explanation

The sag of bending of beam is given by.

δ = \frac{W l^{3}}{48 Y I}

Where W is load, L is length, Y is young's modulus and

I i s \frac{b d^{3}}{12}

(area moment of inertia)

∴ δ = \frac{W l^{3}}{48 Y} \times \frac{12}{b d^{3}} = \frac{W l^{3}}{4 b d^{3} Y}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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