The dimensional formula for a physical quantity `x` is `[M^(-1) L^(3) T^(-2) ]` . The errors in measuring the quantities `M , L , and T,` respectively are `2%, 3% , and 4%`. The maximum percentage of error that occurs in measuring the quantity `x` is

Options

A. `12%`
B. `16%`
C. `17%`
D. `19%`

Answer

D

Explanation

`X=M^(-1)L^(3)T^(-2)`
`(dM)/(M)xx100=2%, (dL)/(L)xx100=3%, (dT)/(T)xx100=4%`
`"Maximum percentage error in X"=(DeltaM)/(M)xx100+3(DeltaL)/(L)xx100+2(DeltaT)/(T)xx100=2+(3xx3)+(2xx4)=2+9+8`
`"Maximum error in X"=19%`