Find the value of ' n ' in the given equation P= ^n v^2 where ' P ' is the pressure, ' ' density and ' v ' velocity.

Step-by-step solution

The dimensional formula for pressure P is [M L⁻¹ T⁻²] . The dimensional formula for density is [M L⁻³] . The dimensional formula for velocity v is [L T⁻¹] . Substituting these into the equation P = ^n v^2 , we get: [M L⁻¹ T⁻²] = [M L⁻³]^n [L T⁻¹]^2 [M L⁻¹ T⁻²] = [M^n L^ -3n ] [L^2 T⁻²] [M L⁻¹ T⁻²] = [M^n L^ -3n+2 T⁻²] Comparing the powers of M on both sides, we get n = 1 . Checking the powers of L : -1 = -3n + 2 3n = 3 n = 1 . Checking the powers of T : -2 = -2 , which is consistent. Answer: n =1