Question

If an object of mass m moves with a uniform speed v along a circular path of radius r, its
acceleration is?​

Answer 1

Solution :

Let the required expression be F=amxvyrz

where a is a dimensionless constant .

x,y, z are powers on m,v and r respectively.

According to the principle of dimensional homogeneity.

[F]=[m]x[v]y[r]z

⇒[M1L1T−2]=[M]x[LT−1]y[L]z

[M1L1T−2]=[MxLy+zT−y]

On equating the dimensions on both sides, we have x=1

y+z=1

and y=2

So that z=-1

Thus the expression for F is F=amv2r−1

orF=amv2r

Dimensionless constant a, in this case is 1.

F=mv2r

The force F is said to be the centripetal force .

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Answer 2

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