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Physics · MECHANICAL PROPERTIES OF SOLIDS
हिन्दीA rectangular horizontal beam of length \( l \), breadth \( b \), and depth \( d \) is supported near its ends and loaded at the centre by a weight \( W \). If the depth of the beam is doubled while its breadth is halved, keeping the load, length, and Young's modulus constant, the sag \( \delta \) at the centre becomes:
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Correct answer · Option C
\( \delta / 4 \)
Explanation
Sag \( \delta = \frac{W l^3}{4 b d^3 Y} \). When \( b' = b/2 \) and \( d' = 2d \), \( \delta' = \frac{W l^3}{4 (b/2) (2d)^3 Y} = \frac{W l^3}{4 (b/2)(8 d^3) Y} = \frac{\delta}{4} \).
