Question

The centripetal force acting on a particle revolving in a circular path depends upon the velocity of the particle (v) and radius of circle (r). Using dimensional method establish the formula for the centripetal acceleration (a).​

Answer 1

Answer:

Correct option is

A

F=

r

mv

2

(where k=1)

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

Answer:

The centripetal force F acting on a particle moving uniformly in a circle may depend upon mass ( m ) , velocity ( v ) and radius ( r )of the circle .