The relative density of a material of a body is found by weighing it first in air and then in water. If the weight of he body in air is `W_(1) = 8.00 +- N` and the weight in water is `W_(2) = 6.00 +- 0.05 N`, then the relative density `rho_(r ) = W_(1)//( W_(1) - W_(2))` with the maximum permissible eror is

Options

A. `4.00 +- 0.62%`
B. `4.00 +- 0.82%`
C. `4.00 +- 3.2%`
D. `4.00+- 5.62%`

Answer

D

Explanation

Relative density `rho_(r ) = (W_(1))/( W_(1) - W_(2)) = ( 8.00) /( 8.00 - 6.00) = 4.00`
`( Delta rho_(r))/( rho_(r )) xx 100 = ( Delta W_(1))/( W_(1)) xx 100 + ( Delta (W_(1) - W_(2)))/( W_(1) - W_(2)) xx 100`
` = ( 0.05)/( 8.00) xx 100 + ( 0.05 + 0.05)/( 2) xx 100 = 5.62%`
:. `rho_(r ) = 4.00 +- 5.62%`