JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Elasticity & SHM

The Young's modulus of a steel wire of length 6 m and cross-sectional area

3 mm^{2}

, is

2 \times 1 0^{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 wire is (Take

g

on the earth

= 10 m / s^{2}

(A)1 cm
(B)1 mm
(C)0.1 mm✓ Correct
(D)0.1 cm

Answer: (C)

Solution

On the planet the gravitational acceleration is

g^{'} = \frac{10}{4} = 2.5 m s^{- 2}

, so the tension in the wire is

F = m g^{'} = 4 \times 2.5 = 10

N. The elongation follows from

Δ L = \frac{F L}{A Y} = \frac{10 \times 6}{( 3 \times 1 0 ^{- 6} ) ( 2 \times 1 0 ^{11} )} = \frac{60}{6 \times 1 0 ^{5}} = 1 0^{- 4}

m. The wire stretches by

0.1

mm.

JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Single correct option

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JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Elasticity & SHM

Solution

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