Question

A thin rod of negligible mass and area of cross-section $4 \times 10^{-6 }m^2$, suspended vertically from one end, has a length of 0.5 m at $100^{\circ}C$. The rod is cooled to 0^{\circ}C[/tex], but prevented from contracting by attaching a mass at the lower end. Find the mass. [Given, for the rod, Young’s modulus = $10^{11} N/m^2$, coefficient of linear expansion = $10^{-5} /K$ and g = $10 m/s^2$.

Answer 1

Answer:

The decrease in length of the Rod on cooling is 

ΔL=LαΔT

ΔL=0.5×10−5×100

ΔL=5×10−4m

(1) If rod in presented from contiacting, the mass m is attached at lover and must increase in length by an amount ΔL=5×10−4m

r=AΔLmgL

r m=g Lr AΔL=10×0.51011×4×10−6×5×10−4

m=40 kg

(2) Energy stored in Rod is

u=21F×ΔL

u=21mgΔL=21×40×10×5×10−4

u=0.1 J

(B) (i) 40kg, (ii) 0.1J