A vertical metal cylinder of radius 2 cm and length 2 m is fixed at the lower end and a load of 100 kg is put on it. Find (a) the stress (b) the strain and (c) the compression of the cylinder. Young modulus of the metal = $2 \times 10^{11} N m^{- 2}$ .

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Solution

r = 2 cm

$\Rightarrow A = π r^{2} = 4 π c m^{2}$

= $4 π \times 10^{- 4} m^{2}$

L= 2 m

m = 100 kg

Y = $2 \times 10^{11} N / m^{2}$

(a) $ρ = s t r e s s = \frac{m g}{A}$

= $\frac{(100 \times 10)}{(4 π \times 10^{- 4})}$

$= 7.96 \times 10^{5} N / m^{2}$

(b) c = strain

= $\frac{ρ}{Y} = \frac{(97.96 \times 10^{5})}{(2 \times 10^{11})}$

= $4 \times 10^{- 6}$

(c) Compression $Δ L = e L$

= $4 \times 10^{- 6} \times 2 = 8 \times 10^{- 6} m$

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A vertical metal cylinder of radius 2 cm and length 2 m is fixed at the lower end and a load of 100 kg is put on it. Find (a) the stress (b) the strain and (c) the compression of the cylinder. Young modulus of the metal = 2×1011Nm−2.

r = 2 cm ⇒A=πr2=4πcm2 = 4π×10−4m2 L= 2 m m = 100 kg Y = 2×1011N/m2 (a) ρ=stress=mgA = (100×10)(4π×10−4) =7.96×105N/m2 (b) c = strain = ρY=(97.96×105)(2×1011) = 4×10−6 (c) Compression ΔL=eL = 4×10−6×2=8×10−6m

A vertical metal cylinder of radius 2 cm and length 2 m is fixed at the lower end and a load of 100 kg is put on it. Find (a) the stress (b) the strain and (c) the compression of the cylinder. Young modulus of the metal = $2 \times 10^{11} N m^{- 2}$ .