if `rho` is the density of the meterial of a wire and `sigma` is the breaking stress. The greatest length of the wire that can hang freely without breaking is

Options

A. `(p)/(rho g)`
B. `(p)/(2rho g)`
C. `(2p)/(rho g)`
D. None of these

Answer

A

Explanation

Maximum stress `= ("Maximum weight")/(Cross-sectional area")`
Now, maximum weight of steel wire = Volume `xx` Density `xx` g
`=A l rho g`
where, l is the maximum length of steel wire that can hang vertically without breaking, `rho` is the density of steel and A is the cross-sectional area of steel wire.
`therefore` Maximum stress, `p= (Al rho g)/(A)= l rho g`
`therefore l=(p)/(rho g)`