The Young’s modulus of a steel wire of length 6 m and cross-sectional area is . The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the wire. The acceleration due to gravity on the planet is of i

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Solution

Q.
The Young’s modulus of a steel wire of length 6 m and cross-sectional area $3 {mm}^{2}$ is $2 \times 10^{11} {N/m}^{2}$ . The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the Earth. The elongation of the wire is (Take g on the Earth $= 10 {m/s}^{2}$ ) [2023]

1 1 cm

2 1 mm

3 0.1 mm

4 0.1 cm

Ans.
(3)

$Tension (F) = m g = 4 \times \frac{10}{4} = 10 N$

$Δ Y = \frac{F L}{A Y} = \frac{10 \times 6}{3 \times 10^{- 6} \times 2 \times 10^{11}} = 10^{- 4} m = 0.1 mm$

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