A thin 1 m long rod has a radius of 5 mm . A force of $50 \pi \mathrm{kN}$ is applied at one end to

Question

A thin 1 m long rod has a radius of 5 mm . A force of $50 \pi \mathrm{kN}$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm , which of the following statements is false?\

Professor PC Thomas Classes · Answer

(a) : Here, $L=1 \mathrm{~m}$\ $r=5 \mathrm{~mm}=5 	imes 10^{-3} \mathrm{~m}$\ $F=50 \pi \mathrm{kN}$, L.C. of all lengths $=0.01 \mathrm{~mm}$\ $Y=$ ?\ $Y=\frac{	ext { Stress }}{	ext { Stain }}=\frac{F L}{A l}=\frac{F L}{\pi r^{2} l}$\ $Y=\frac{50 \pi 	imes 10^{3}}{\pi\left(5 	imes 10^{-3}ight)^{2}} 	imes \frac{L}{l}=2 	imes 10^{9} 	imes \frac{L}{l}=\frac{2 	imes 10^{9}}{l}$\ $\frac{\Delta Y}{Y}=2 \frac{\Delta r}{r}+\frac{\Delta L}{L}+\frac{\Delta l}{l}$\