Question

velocity of waves along a string is v= √ T/m,Where 'T' the tension in the string and 'm' is mass per unit length of the string.Show this quation is dimentionaly correct

Answer 1

Answer:

Given:

Equation for velocity of wave in string has been given.

To find:

Whether this Equation is dimensionally correct or not.

Calculation:

Dimensional analysis is performed by matching the LHS AND RHS.

LHS

Velocity has the following dimension:

V = [ L T^(-1) ] ..........(1)

RHS

√(T/m) ,

where T => Tension and m => mass per unit length

Tensions is actually force ,

Mass per unit length can be represented as M/L

Continuing with the Calculation:

√(T/m)

= √ [ {M L T^(-2)}/ { M L^(-1)} ]

= √[ L² T^(-2)]

= L T^(-1) .........(2)

Since (1) = (2) , we have LHS = RHS.

Hence the Equation I dimensionally correct.

Answer 2

Answer:

velocity of wave = √T/m

m =>mass per unit length

T is tensile force

Dimension of T => ML T^-2

Dimension of m => M L^-1

Velocity dimension = √[(MLT^-2)/ML^-1]

= √(L^2 T^-2)

= L T^-1

Which is dimension of velocity

hence eq is dimensionally correct

#answerwithquality #BAL