Find the expression for centripetal force …
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- Find the expression for centripetal force if it depends upon mass of the body, and the radius of the circular path?
Posted by Lochan Soni 8 years, 7 months ago
- 2 answers
Payal Singh 8 years, 6 months ago
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.
Let F = k ma vb rc…..... (i)
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] = Ma [LT-1]bLc
=> [M1L1T-2] = MaLbLcT-b
=> [M1L1T-2] = MaLb+c T-b
on comparing both sides we get
a = 1
b+c = 1
-b = -2 => b = 2
Then c = -1
Onputting these values in (i),
we get
F = k m1 v2 r-1
Or
{tex}F = k {mv^2\over r}{/tex}
This is the required relation for centripetal force.
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Abhishek Kumar 6 years, 6 months ago
0Thank You