Question

a particle of 0.5kg is rotating uniformly in a circle of radius 6cm at 300rev/minute what will be the centripetal force acting on the body?​

Answer 1

Given :

▪ Mass of the particle = 0.5kg

▪ Radius of circular path = 6cm

▪ Frequancy of rotation = 300rpm

To Find :

▪ Centripetal force acting on the particle.

Formula :

⏭ Formula of centripetal force acting on the body of mass m, moving with velocity v in the circular path of radius r is given by

$\bigstar\:\underline{\boxed{\bf{\gray{F_c=\dfrac{mv^2}{r}}}}}$

Conversion :

➡ Radius = 6cm = 0.06m

➡ Frequency = 300rpm = 5rps

Calculation :

$\implies\sf\:F_c=\dfrac{mv^2}{r}\\ \\ \implies\sf\:F_c=\dfrac{m(r\omega)^2}{r}\\ \\ \implies\sf\:F_c=mr\omega^2\\ \\ \implies\sf\:F_c=mr(2\pi f)^2\\ \\ \implies\bf\red{F_c=4{\pi}^2mrf^2}\\ \\ \implies\sf\:F_c=4\times (3.14)^2\times 0.5\times 0.06\times (5)^2\\ \\ \implies\underline{\boxed{\bf{\green{F_c=29.57N}}}}$