Question

a ball of mass 500gm is tied to one end of a rope of length 3m. The other end is fixed and the ball is now moving along a horizontal circle with uniform angular speed of 2rev/s. The tension in the rope will be?​

Answer 1

Given :

Mass of ball = 500g = 0.5kg

Radius of circular path = 3m

Frequency of revolution = 2 rps

To Find :

Tension in the rope.

Solution :

❖ Centripetal force is not a new kind of force. The material forces such as tension, gravitational force, electrical force, friction etc., may act as the centripetal force in any circular motion.

• Centripetal force us the name of any force that provides radial inward acceleration to a body in circular motion.

$\sf:\implies\:F_c=\dfrac{mv^2}{r}$

• m denotes mass

• v denotes linear velocity

• r denotes radius

$\sf:\implies\:F_c=\dfrac{m(r\omega)^2}{r}$

where ω denotes angular velocity

$\sf:\implies\:F_c=\dfrac{mr^2(2\pi f)^2}{r}$

$\sf:\implies\:F_c=4\pi^2mrf^2$

By substituting the given values;

$\sf:\implies\:F_c=4(3.14)^2\times0.5\times3\times(2)^2$

$\sf:\implies\:F_c=40\times 1.5\times 4$

$\sf:\implies\:F_c=40\times6$

$:\implies\:\underline{\boxed{\bf{\orange{F_c=240\:N}}}}$