Question

the magnitude of change in velocity of a particle having speed v is, v during a time interval △ t while moving in a uniform circular motion.The magnitude of average force on the particle is proportional to:

Answer 1

As we know rate of change of velocity is acceleration, $a_{avg}=\frac{changeinvelocity}{timeperiod}=\frac{\Delta v}{\Delta t}$

Average force, $F_{avg}=m{a}_{avg}=\frac{mv}{\Delta t}$

So, $F_{avg}\propto \frac{v}{\Delta t}$

And for circular motion force will be,

$F=\frac{m{v}^2}{r}$

$F\propto v^2$

Hence, we can say, The magnitude of average force on the particle is proportional to: velocity.