StemCET Logo

Physics Question 31 – JEE-MAIN 2025

← Back
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×1011 Nm−2, where the value of P is: (Take g=3π m/s2)

Young's modulus is a measure of the stiffness of an elastic material and is defined as the ratio of stress to strain.

Step 1: Identify given parameters and convert to SI units✦ Active

The given parameters are: original length L=3 m, radius r=3 mm=3×10−3 m, extension ΔL=0.1 mm=1×10−4 m, mass m=50 kg, and acceleration due to gravity g=3π m/s2.

Step 2: Calculate the force and cross-sectional area○ Expand

The force applied is due to the mass, so F=mg. The cross-sectional area of the wire is A=πr2.

F=50 kg×3π m/s2=150π N A=π(3×10−3 m)2=9π×10−6 m2
Step 3: Calculate Young's modulus and determine P○ Expand

Young's modulus Y is given by the formula Y=F/AΔL/L=F×LA×ΔL. Substitute the calculated values.

Y=150π N×3 m9π×10−6 m2×1×10−4 m=450π9π×10−10=50×1010=5×1011 Nm−2

Comparing this with P×1011 Nm−2, we find P=5.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.