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COMEDK2015PhysicsMechanical Properties of Solids

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 10¹¹ ~Pa , what will be roughly the increase in the length of the cable while lifting the block? (Take, g=10 ~ms ⁻² )

Options

  1. A0.75 ~cm
  2. B1.25 ~cm
  3. C1.75 ~cm
  4. D2.50 ~cm

Correct answer

C. 1.75 ~cm

Step-by-step solution

Given, length, l=11 ~m Radius, r=2 ~cm Radius, =2 10⁻² ~m Mass, m=40 tons =4 10⁴ ~kg Increase in length, l= ? We know that, Young's modulus, aligned Y &= m g l r²( l) l &= m g l r² Y &= 4 10⁴ 10 11 3.14 (2 10⁻² )² 2 10¹¹ &=1.75 10⁻² ~m &=1.75 ~cm aligned

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