A thick rope of density 1.5 xx 10 ^(3) kg m ^(-3)and Young's modulus 5 xx 10 ^(6) Nm ^(-2), 8 m in length when hung from the ceiling of room the increase in its length due to its own weight is .......... (g = 10 ms ^(-2))

A thick rope of density 1.5 xx 10 ^(3) kg m ^(-3)and Young's modulus 5

1.	A thick rope of density 1.5 xx 10 ^(3) kg m ^(-3)and Young's modulus 5 xx 10 ^(6) Nm ^(-2), 8 m in length when hung from the ceiling of room the increase in its length due to its own weight is .......... (g = 10 ms ^(-2))
Answer» `9.6 xx 10 ^(-5) m` `19.2 xx 10 ^(-7) m` `9.6m` `9.6 xx 10^(-2) m` Solution :If the ength of rope is l, the increase in LENGTH in rope is only `(l)/(2).` Now `Y = F/A xx ((l)/(2) )/( Delta L ) = (Wl )/( 2 A Delta l ) [ because F = W`weight] `THEREFORE Y = (mgl )/( 2 A Delta l ) = (A l rho gl )/( 2 A Delta l ) ""[because m = A l rho ]` `therefore Y = (rho g l ^(2))/( 2 Delta l )` `therefore DL = (rho g l ^(2))/( 2Y) =(1.5 xx10 ^(3) xx 10 xx (8) ^(2))/( 2 xx 5 xx 10 6^(6))` `therefore Delta l =9.6 xx 10 ^(-2) m`