The compressibility of a material is B.A cube of side 'a' is made with this material. If a uniform pressure P is applied on the cube from all the sides the fractional change in its length will be

Options

A. 2P/B
B. PB/3
C. PB
D. B/3P

Answer

B

Explanation

`k'=(1)/(k)=(1)/(v(dp)/(dv))=(dv)/(dp)`
`(dv)/(v) = Pk' = PB " " ` …(i)
`v =a^(3)`
Differenciate above equation,
`(dv)/(v)=3(Delta a)/(a)`
Substitute `(dv)/(v)` in equation no (i),
`3 (Delta a)/(a) = PB`
`(Delta a)/(a)=(PB)/(3)`