Assume the density of brass weights to be `8 g cm^(-3)` and that of air to be `0.0012g cm^(-3)`. What fractional error arises from neglecting buoyancy of air in weighing an object of density `3.4 g cm^(-1)` on a beam balance?

Options

A. `2xx10^(-1)`
B. `2xx10^(-2)`
C. `2xx10^(-3)`
D. `2xx10^(-4)`

Answer

D

Explanation

Let `m gwt` be the weight of object in vacuum.
Volume of object = `(m)/(3.4)`
weight of air displaced by object = `m/3.4 xx 0.0012`
Volume of brass weight =` m/8`
weight of air displaced by brass weights
`=m/8 xx 0.0012`
Error=differecne in buouancy
`=0.0012[1/3.4-1/8]`
Fractional error = `(0.0012 xx 4.6)/(3.4xx8) = 2 xx 10^(-4)`.