A ball is whirled on the end of a string in a horizontal circle of radius R at a speed v. Complete the following statement: The centripetal acceleration of the ball can be increased by a factor of 8 by ________.
Question
Question
A ball is whirled on the end of a string in a horizontal circle of radius R at a speed v. Complete the following statement: The centripetal acceleration of the ball can be increased by a factor of 8 by ________.
Answer:
Explanation:
The formula of the centripetal acceleration is given by
[tex]a=\frac{v^{2}}{R}[/tex]
The centripetal acceleration is increased by 8 times, it means the velocity is doubled and the radius is halved.
Explanation:
When an object moves in a circular path, centripetal force acts on it. The magnitude of centripetal acceleration is given by formula :
[tex]a=\dfrac{v^2}{r}[/tex]
Here,
v is the speed of the ball in circular path
r is the radius of circular path
The centripetal acceleration is inversely proportional to the radius of the circular path. To increase the centripetal acceleration by a factor of 8, the radius must decrease by a factor of 8 keeping speed constant.