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 
, where the value of P is: (Take 
)
Text Solution
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Let's break down the solution step by step:
First, note the given values:
Length of the wire, 
Radius of the wire, 
Extension of the wire,
Mass attached, 
Acceleration due to gravity, 
The force (weight) acting on the wire is:
Next, calculate the cross-sectional area, A, of the wire:
Young's modulus, E, is given by:
Substitute the values into the formula:
Simplify step by step:
Multiply in the numerator:
Multiply in the denominator:
Cancel the common factor 
in the numerator and denominator:
Divide 450 by 9:
The problem states that Young's modulus can be expressed as 
. Here we have:
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