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CBSE Class 12-science Answered

An aluminum bar 100 cm in length 2cm in width 0.5cm in thickness is supported on two horizontal knife edges 60 cm of a part.if the middle of the beam rise by point 6cm when two equal rates of 1 kg are attached at two end. calculate young modulus of aluminum
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Asked by Mdsimabc | 23 Aug, 2019, 02:44: PM
answered-by-expert Expert Answer
Youngs Modulus Y is obtained from the formula given below using the elevation measured in  uniform bending of beam.
 
begin mathsize 12px style Y space equals space fraction numerator 3 space M space g space a space l squared over denominator 2 space s space b space d cubed end fraction space space................. left parenthesis 1 right parenthesis end style
where M is mass of load applied, M = 1 kg
g is acceleration due to gravity, g = 9.8 m/s2
a is the distance of load applied point from knife edge, a = 20 cm = 20×10-2 m
l is the distance between knife edge, l = 60 cm = 60×10-2 m
s is the elevation (rise of the middle point of beam), s = 6 cm = 6×10-2 m
b is breadth of the beam , b = 2 cm = 2×10-2 m
d is thickness of beam,  d = 0.5 cm = 5×10-3 m
 
By substituting all the values in the formula (1), we get Y ≈7 ×109 N/m2   = 7 GPa
 
( Youngs modulus of Aluminium ~70GPa, but by solving this question we get only 7 GPa.
 I suspect the elevation (rise of the mid point of beam) value 6 cm is not realistic,
6 mm may be reasonable.  if we consider this elevation as 6 mm, then we get Youngs modulus 70 GPa )
Answered by Thiyagarajan K | 23 Aug, 2019, 09:32: PM

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