Question

The force acting on a body depends upon the mass,velocity and radius of the circular path.Obtain a relation for force using dimensional analysis.​

Answer 1

Answer:

Let F=k(m)

x

(v)

y

(r)

z

Here, k is a dimensionless constant of proportionality. Writing the dimensions of RHS and LHS in Eq. (i), we have

[MLT

2

]=[M]

x

[LT

−1

]

y

[L]

z

=[M

x

L

y+z

T

−y

]

Equation the powers of M, L and T of both sides, we have,

x=1,y=2andy+z=1

or z=1−y=−1

Putting the values in Eq. (i), we get

F=kmv

2

r

−1

=k

r

mv

2

F=

r

mv

2

(where k=1)