Question

Show dimensionally that the centripetal force acting on a particle of mass m moving in a circle of radius r moving with a velocity v is F=mv²/r........answer properly..thank you

Answer 1

Answer:

Centripetal force acting on a particle of mass m moving in a circle of radius r moving with a velocity v dimensionally can be given by ;

$f = \frac{mv {}^{2} }{r} \\ \\ ma \: = \frac{mv {}^{2} }{r} \\ \\ \frac{mv}{t} = \frac{mr {}^{2} }{rt {}^{2} } \: \: \: (r = diplacement) \\ \\ \frac{mr}{t {}^{2} } = \frac{m r }{t {}^{2} } \\ \\ mlt {}^{ - 2} = mlt {}^{ - 2}$

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