Question

f = 1/2L * √(T/m) find dimension of m

Answer 1

Answer:

In thin string of length L, bound tightly at its two ends, transverse waves can be created.  Let the tension in the string be T and  mass per unit length be m.

   frequency of oscillation (SHM) = f = 1/2L  * √(T/m)

one can use the dimensional analysis:  

 f = [ T⁻¹ ]

L = [ L ]

T = force = [ M L T⁻² ]

m = [ M L⁻¹ ]

so RHS = [ T⁻¹ ] = LHS.