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.

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.

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.