The Young's modulus of a rope of 10 ~m length and having diameter of 2 ~cm is 20.0 10¹¹ dyne / cm ^2 . If the elongation produced in the rope is 1 ~cm , the force applied on the rope is

Step-by-step solution

Here, Length of the rope, L=10 ~m Diameter of the rope, D=2 ~cm Radius of the rope, r= D 2 =1 ~cm =10⁻² ~m Young's modulus of the rope aligned Y & =20 10¹¹ dyne cm ^2 =20 10¹¹ 10⁻⁵ (10⁻² )^2 N m ^2 & =20 10¹¹ 10⁻⁵ ~N 10⁻⁴ ~m ^2 =20 10¹⁰ N m ^2 aligned Elongation of rope, L=1 ~cm =10⁻² ~m As aligned Y & = F / A L / L or F=Y A L L = Y r^2 L L & = 20 10¹⁰ 3.14 (10⁻² )^2 10⁻² 10 & =6.28 10^4 ~N aligned