Respuesta :
Explanation:
The centripetal acceleration of the ball that is whirled on the end of a string in a horizontal circle of radius R at constant speed v, is given by :
[tex]a=\dfrac{v^2}{R}[/tex]
Option (1) : Keeping the speed fixed and decreasing the radius by a factor of 9
[tex]a=\dfrac{v^2}{R/9}[/tex]
[tex]a=\dfrac{9v^2}{R}[/tex]
The centripetal acceleration of the ball by a factor of 9.
Option (2) : Keeping the radius fixed and increasing the speed by a factor of 3
[tex]a=\dfrac{(3v)^2}{R}[/tex]
[tex]a=\dfrac{9v^2}{R}[/tex]
Acceleration increases.
Option (3) : Decreasing both the radius and the speed by a factor of 9.
[tex]a=\dfrac{(v/9)^2}{R/9}[/tex]
[tex]a=\dfrac{(v)^2}{9R}[/tex]
Acceleration decreases by a factor of 9.
Option (4) : Keeping the radius fixed and increasing the speed by a factor of 9
[tex]a=\dfrac{(3v)^2}{R}[/tex]
[tex]a=\dfrac{9v^2}{R}[/tex]
Acceleration increases.
Option (5) : Increasing both the radius and the speed by a factor of 9
[tex]a=\dfrac{(9v)^2}{9R}[/tex]
[tex]a=\dfrac{9v^2}{R}[/tex]
Acceleration increases.
Option (6) : Keeping the speed fixed and increasing the radius by a factor of 9
[tex]a=\dfrac{(v)^2}{9R}[/tex]
[tex]a=\dfrac{9v^2}{R}[/tex]
Acceleration increases.
Hence, this is the required solution.
