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 th…

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 10^11 Nm^-2, where the value of P is: (Take g=3 m/s^2 )

Accepted Answer

Correct answer: D. (d) Let's break down the solution step by step: First, note the given values: Length of the wire, L=3 m Radius of the wire, r=3 mm=3 10^-3 m Extension of the wire, L=0.1 mm=1 10^-4 m Mass attached, m=50 kg Acceleration due to gravity, g=3 m/s^2 The force (weight) acting on the wire is: F= mg=50 3 =150 N Next, calculate the cross-sectional area, A, of the wire: A= r^2= (3 10^-3)^2= 9 10^-6=9 Young's modulus, E, is given by: E= FLA L Substitute the values into the formula: E= (150 ) 3(9 10^-6) (1 10^-4) Simplify step by step: Multiply in the numerator: 150 3=450 Multiply in the denominator: 9 10^-6 1 10^-4=9 10^-10 Cancel the common factor in the numerator and denominator: E= 4509 10^-10 Divide 450 by 9: E= 4509 110^-10=50 10^10=5 10^11 Nm^- : The problem states that Young's modulus can be expressed as P 10^11 Nm^-2. Here we have: P=5

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

Solution

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