Question

DERIVE THE EXPRESSION FOR CENTRIPETAL FORCE (F) WHICH DEPENDS ON • MASS (m) • RADIUS OF THE ORBIT (r) • VELOCITY OF THE BODY (v) USING DIMENSIONS.
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please give full steps if you know ​

Answer 1

Answer:

F = m (v²) /r

Explanation:

Solution :

Centripetal Force is the Force acting on a body moving in a circular path.

Centripetal Force depends on mass of body, Speed of the body and the radius of circular path.. So let

Mass of body be 'm' Speed of body be 'v' Radius of path

F Q ma vb rc

[M'L' T-²] = [M^) [LT"^"]" [L]" = [ M² (b+² [b]

Comparing L.H.S & R.H.S.

a = 1

b + c = 1

-b = -2 => b = 2

:. c = 1 - b

= 1- 2

= -1

F = m ^ (1) * v ^ 2 * r ^ - 1

F = mv²/r