A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to

Question

A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to (A) Y2 (B) Y (C) (1/Y) (D) (1/Y2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-dlyaafzh74nf.png" /> δ = Depression in the beam Y = Young's Modulus W = Load Applied L = Length of the beam b = width of the beam d = thickness of the beam δ=(WL3/4 Ybd3) ∴ δ propto (1/Y)

Q. A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to

$Y^{2}$

$Y$

$\frac{1}{Y}$

$\frac{1}{Y ^{2}}$

$δ$ = Depression in the beam
$Y$ = Young's Modulus
$W$ = Load Applied
$L$ = Length of the beam
$b$ = width of the beam
$d$ = thickness of the beam
$δ = \frac{W L ^{3}}{4 Yb d ^{3}}$
$∴ δ \propto \frac{1}{Y}$

Q. A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to

Y2

Y

Y1​

Y21​

δ = Depression in the beam Y = Young's Modulus W = Load Applied L = Length of the beam b = width of the beam d = thickness of the beam δ=4Ybd3WL3​ ∴δ∝Y1​

$Y^{2}$

$Y$

$\frac{1}{Y}$

$\frac{1}{Y ^{2}}$

$δ$ = Depression in the beam
$Y$ = Young's Modulus
$W$ = Load Applied
$L$ = Length of the beam
$b$ = width of the beam
$d$ = thickness of the beam
$δ = \frac{W L ^{3}}{4 Yb d ^{3}}$
$∴ δ \propto \frac{1}{Y}$