Question

Deduce formula :frequency proportional to length ,mass and tension

Answer 1

TOPIC :- DIMRNSIONAL ANALYSIS

SOLUTIONS

Given,

frequency is directly proportional to length , mass and tension. Hence, frequency can be written as

$f = {L}^{a} {M}^{b} {T}^{c}$.........(I)

Now,

Dimension of L = [L]

Dimension of M = [M]

Dimension of T = $ML{T}^{ - 2}$

Dimension of f = ${T}^{ - 1}$

Now, for the above formula of frequency to be correct, the equation should also be dimensionally correct.

There fore ,

dimension of LHS = dimension of RHS

=> {T}^{ - 1} = ${L}^{a} {M}^{b} {(ML{T}^{ - 2}) }^{c}$

=> {T}^{ - 1} = ${L}^{a + c} {M}^{b + c} {T}^{ - 2c}$

Comparing both sides, we get

=> a + c = 0

b + c = 0

-2c = -1

=> c = 1/2

and a = b = -1/2.

putting these values in equation (I)

f = k √T/√L√M