A wire is loaded by a weight of density `9g//cm^(3)` and stretched to a length of 98 cm. On immersing the weight in water the length shortens by 2.5 mm. Then the original length of the wire will be
`[rho_(w)=1 gm//cm^(3)]`

Options

A. 95.75 cm
B. 98.75 cm
C. 90. 75 cm
D. 85.75 cm

Answer

A

Explanation

`L+X=98 " " therefore x=98-L`
`L+y=98-0.25 " " therefore y=98-L-0.25`
`T_(1) prop x and T_(2) prop y`
`(T_(1)-T_(2))/(T_(1))=(x-y)/(x)=(0.25)/(98-L)`
`(V rho g)/(V rho_(1)g)=(0.25)/(98-L)`
`(rho)/(rho_(1))=(0.25)/(98-L)`