Question 51: Work, Energy and Power & Circular Motion

Question

A ball of mass $0.5 \mathrm{~kg}$ is attached to a string of length $50 \mathrm{~cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 \mathrm{~N}$. The maximum possible value of angular velocity of the ball in $\mathrm{rad} / \mathrm{s}$ is, :

Accepted Answer

To find the maximum possible angular velocity (ÃÂ) of the ball, we need to consider the maximum tension the string can bear without breaking. This tension provides the centripetal force needed to keep the ball in a circular path.
The centripetal force (F
c
) required for circular motion is given by the formula:
$ F_{c} = m r \omega^2 $
Where:
m = mass of the ball (0.5 kg)
r = radius of the circle (0.5 m, since 50 cm = 0.5 m)
ÃÂ = angular velocity in rad/s
The maximum tension the string can bear is also the maximum centripetal force (F
c,max
) that can be provided by the string, which is 400 N.
Now we can set up the equation with the given values:
$ 400 = 0.5 	imes 0.5 	imes \omega^2 $
$$ \Rightarrow $$ $ 400 = 0.25 	imes \omega^2 $
$$ \Rightarrow $$ $ \omega^2 = \frac{400}{0.25} $
$$ \Rightarrow $$ $ \omega^2 = 1600 $
$$ \Rightarrow $$ $ \omega = \sqrt{1600} $
$$ \Rightarrow $$ $ \omega = 40 \, \mathrm{rad/s} $
Therefore, the maximum possible angular velocity of the ball is 40 rad/s, which corresponds to Option C.

Answer

1600

Answer

20

Answer

40

Answer

1000

Work, Energy and Power & Circular Motion

Choose the correct answer: