Question

Obtain an expression for bulk modulus. State SI unit and dimensions of 'K'.

Answer 1

bulk modulus is the ratio of the change in pressure to the fractional volume compression.
actually, bulk elastic properties of a material is used to determine how much it will compress under a given amount of external pressure.

from above definition,
bulk modulus, K = ∆P/(∆V/V)
where ∆P is the change in pressure , ∆V is change in volume and V is initial volume.

so, S.I unit of bulk modulus is N/m² or Pascal
dimension of bulk modulus is $[ML^{-1}T^{-2}]$

Answer 2

HEY DEAR ... ✌️

__________________________

__________________________

=) With in the elastic limit , upto which Hooke's law is applicable , the ratio of the normal stress to the volume strain is called the 'bulk modulus' of the material of the body . It is denoted by B .


Let the initial volume of the body be V which changes by ∆V when a pressure p is applied . (when the pressure increases the volume decreases and vice-versa.) Then

normal stress = p , volume strain = - ∆V / V .

.-. bulk modulus of the material of the body is

B = normal stress / volume strain

B = p / -∆V/V

B = -pV / ∆V .

If p is positive , then ∆V will be negative and if p is negative , then ∆V will be positive . The negative sign in the above formula shows that B is positive . On compressing under same pressure , larger volume strain is produced in gases but very little in liquids and solids .

The SI unit of B is 'newton/metere^2' (Nm^-2) or 'pascal' (Pa) and it's dimensional formula is [ML^-1T^-2] .

________________________

________________________

HOPE , IT HELPS ... ✌️