the force of F acting on a body moving in circular path depends on mass of the body (m) velocity (v) and radius (r) of the circulation path.obtain the expression for the force by dimensional analysis method ( take value of k =1)
Answers
Answer:The force F acting on a body moving in a circular path depends on mass of the body (m) velocity(v) and radius (r) of the circular path.
The centripetal force, F acting on a particle moving uniformly in a circle depend upon the mass (m), velocity (v) and radius (r) of the circle.
The formula for F using the method of dimensions.
Where, k is the dimensionless constant of proportionality, and a, b, c are the powers of m, v, r respectively.
On writing the dimensions of various quantities in (i),
we get
[M¹L¹T‐²] = M^a [LT‐¹]^b L^c
=> [M¹L¹T‐²] = M^a L^b L^c T^-b
=> [M¹L¹T-²] = M^a L^b+c T^-b
on comparing both sides we get
a = 1
b+c = 1
-b = -2 => b = 2
Then c = -1
On putting these values in (i),
we get,
F = k m¹ v¹ r‐¹
Or
F=k(mv²)/r
This is the required relation for centripetal force.
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