The given formula of Young’s modulus of elasticity, Y=
mgL3
4bd3δ
where, Y = Young’s modulus of elasticity, m = mass of the bar, L = length of the bar b = breadth of the bar d = thickness of the bar and δ = depression of the bar. There is no error in the value of the g. The fractional error in the measurement of Y,
ΔY
Y
=
ΔM
M
+3
ΔL
L
+
Δb
b
+3
Δd
d
+
Δδ
δ
Substituting the values in the above expression, we get
ΔY
Y
=
10−3
2
+3
(1×10−3)
1
+
0.1×10−3
4×10−2
+3
(0.01×10−3)
0.4×10−2
+
(0.01×10−3)
5×10−3
ΔY
Y
=0.0155 The fractional error in the measurement of the Young’s modulus is 0.0155.