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Prove: a= v²/r proof: F = …

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Prove: a= v²/r proof: F = ma; F = mv²/r, so, ma= mv²/r; a= v²/r, where, m cancelled on both side. Is it correct? Can we prove like that????

Posted by Nasra Javed 1 year, 1 month ago

CBSE > Class 11 > Physics

1 answers

Anjan Karthi 1 year, 1 month ago

Well, we can't actually, because F = mv2/r is itself a derivative of the equation a = v2/r. But, we have another proof. According to law of conservation of energy, kinetic energy b/w two diametrically opposite points = potential across the points. So, we can write 1/2 m(2v) ^2 (since, vector v across two points are opposite in direction and relative velocity becomes v - (-v) = 2v) = ma (2r) . Therefore, m cancelled on both sides, we get 2v^2 = a (2r) . Therefore, v^2 = ar or, a = v^2/r.

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