Question

A crane with.a steel cable of length $ {11 \,m}$ and radius $ {2.0\, cm}$ is employed to lift a block of concrete of mass 40 tons in a building site. If the Young's Modulus of steel is $ {2.0 \times 10^{11} \, Pa}$, what will be roughly the increase in the length of the cable while lifting the block? (Take $ {g = 10\, ms^{-2}}$)

• A. 0.75 cm
• B. 1.25 cm
• C. 1.75 cm
• D. 2.50 cm

Answer 1

The Correct Option is C

Length of cable, $ { L = 11 \, m}$
radius of cable,$r = {2\, cm = 0.02 \,m}$
Young's modulus of steel, $Y = 2 \times 10^{11} \, { Pa}$
$ {g = 10\, m \,s^{-2}}$ ; increase in length, $ l = ?$
Mass of block, $M = 40 \, {tons} = 40 \times 10^3 \, { kg}$
As , $Y =\frac{\frac{F}{A}}{\frac{l}{L}} = \frac{Mg \times L}{\pi r^{2}\times l}$
$ l = \frac{Mg\times L}{\pi r^{2}\times Y} =\frac{40 \times10^{3}\times10 \times11}{3.14\times\left(0.02\right)^{2}\times2\times10^{11}} $
$= \frac{11}{628} = {0.0175\, m = 1.75 \,cm}$