Question

the centripetal force acting on a particle revolving in a circular path depends upon velocity of the particle v and radius of circle r, using dimension method establish the formula for the centripetal acceleration a. ​

Answer 1

Explanation:

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)

Answer 2

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