Question

Mass depends on Velocity V , Density rho and acceleration g . Show that Mass varies to 6th power of velocity.

Answer 1

M -> V, d (density) and g

 

    Let M (proportional to) Vadbgc

Now Hence M = k Vadbgc  where k is constant of proportionality

[M] = [V]a[d]b[g]c

M1L0T0 = (L1T-1)a(M1L-3)b(L1T-2)c

M1L0T0 = Mb La - 3b + c  T-a - 2c

Comparing the powers,

 

b = 1

a - 3b + c = 0

Hence,

 

a - 3(1) + c = 0

a + c = 3  ...........1

-a - 2c = 0 ............2

 

Solving equations 1 and 2,

a + c =  3

-a - 2c = 0

---------------

     -c = 3

Hence, c = - 3.

Substituting c = -3 in equation 1, we get a = 6.

Thus, M = k V6dg

hence, it can be said that M varies with 6th power of velocity.

Hint: In any type of problems of dimensional analysis where it is given that This quantity depends on so and so... solve by this method always. It would be easier.

 I hope it helped.