Question

3. Assuming that the frequency gamma of a
vibrating string may depend upon i)
applied force (F) ii) length (C) iii) mass
per unit length (m), prove that you gamma, alpha
1
F
IVM
using dimensional analysis.
(related to JIPMER 2001)​

Answer 1

Force =1 /time

f = T ^-1

F unit is kgms ^-2

dimension formula is MlT ^-2

length unit M dim formula is L

mass length is Kgm ^-1

dimensions formula is Ml ^-1

(T ^-1 ) = (MlT ^-2 )^a (l ) ^b (ml -1)c

(T^-1 ) = (M ) ^a+c (L ) ^a+b-c (T )^-2 a

Now a =0

b=0

c=1

a+c =0

1/2 +c =0

c =-1/2

a+b-c =0

1/2 +b -1/2 =0

b =-1

-2a =1

a = 1/2

K F ^1/2 l ^-1 m ^1/2

V = K /L root of f / m is proved