Question

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is \(P \times 10^{11} Nm^{-2}, \) where the value of P is \(:(\text{Take g} = 3\pi \ m/s^2)\)

(1) 5

(2) 10

(3) 25

(4) 2.5

Answer 1

Correct option is : (1) 5

\(\frac{50g}{\pi r ^2} =y. \frac{\Delta \ell}{\ell}\)

\(\frac{50\times 3\pi}{\pi \times (3\times 10^{-3})^2} = P\times 10^{11} \times \frac{0.1 \times 10^{-3}}{3}\)

\(\Rightarrow P = \frac{50\times 3 \times 3}{3^2 \times 10^{-6} \times 10^{11} \times 0.1\times 10^{-3}}\)

\(P = 5\)