The centripetal force acting on a particle moving in circular orbit depends on its mass radius of the circle and the speed of the particle obtain the formula for the centripetal force using the dimensional method
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suppose the force depends on the m,v and r as those of its powers as x,y and z.
Then, let the centripetal force be F=(m^x)×(v^y)×(r^z).
Now, F=[MLT^-2].
again, m=[M],v=[LT^-1] and r=[L]
so, comparing both sides we get,-
x=1, and y+z=1
and, -y=-2=>y=2.
hence F=(m×v^2)/r.where k=1.
Then, let the centripetal force be F=(m^x)×(v^y)×(r^z).
Now, F=[MLT^-2].
again, m=[M],v=[LT^-1] and r=[L]
so, comparing both sides we get,-
x=1, and y+z=1
and, -y=-2=>y=2.
hence F=(m×v^2)/r.where k=1.
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