Question

The relative density of a material is found by weighing the body first in air and then in water . If the weight in air is `( 10.0 +- 0.1) gf` and the weight in water is `( 5.0 +- 0.1) gf`, then the maximum permissible percentage error in relative density is
A. `1`
B. `2`
C. `3`
D. `5`

Answer 1

Correct Answer - D
Relative density ` = (W_(a))/(W_(a) - W_(w)) , rho = (W_(a))/( w)`
where ` rho` is relative density , `W_(a)` is weight in air , and `w` is loss in weight.
`(Delta rho)/( rho) = ( Delta W_(a))/( W_(a)) - ( Delta w)/(w)`
For maximum error , `( Delta rho)/( rho) = (Delta W_(a)) /( W_(a)) + ( Delta w)/( w)`
For maximum percentage error ,
`( Delta rho)/( rho) xx 100 = ( Delta W_(a))/( W_(a)) xx 100 + ( Delta w)/( w) xx 100`
Given ` Delta W_(a) = 0.1 gf and W_(a) = 10.0 gf`
` w = 10.0 - 5.0 = 5.0 gf`
`Delta w = Delta W_(a) + Delta W_(w) = 0.1 + 0.1 = 0.2 gf`
`( Delta rho)/( rho) xx 100 = (( 0.1)/( 10.0)) xx 100 + (( 0.2)/( 5.0)) xx 100 = 1 + 4 = 5 `