Question

If density P, acceleration due to gravity g and frequency v are basic quantity find dimensional of force.​

Answer 1

Given : If density P, acceleration due to gravity g and frequency v are basic quantities.

To find : The dimensional formula of force.

solution : dimensional formula of density, P = [ML¯³]

dimensional formula of acceleration due to gravity, g = [LT¯²]

dimensional formula of frequency, v = [ T¯¹ ]

dimensional formula of force, F = [MLT¯²]

from dimensional analysis,

F = P^xg^yv^z

⇒[MLT¯²] = [ML¯³]^x [LT¯²]^y [T¯¹]^z

⇒[MLT¯²] = [M^x L^(-3x + y) T^(-2y - z)]

on comparing we get,

x = 1,

-3x + y = 1 ⇒y = 1 + 3x = 1 + 3 = 4

-2y - z = -2 ⇒2y + z = 2 ⇒z = 2 - 2y = -6

Therefore dimensional formula of force, F = Pg⁴/f^6

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