Respuesta :
Explanation:
(a) On circular path, an object moves with centripetal acceleration which is given by :
[tex]a=\dfrac{v^2}{r}[/tex]
v is the velocity of the object
r is the radius of circular track
[tex]v=\dfrac{2\pi r}{T}[/tex]
[tex]a=\dfrac{4\pi^2 r}{T^2}[/tex]
Acceleration is directly proportional to the radius of track and inversely proportional to the period of rotation. If the radius of the circle halves and the period of rotation stays the same.
[tex]a=\dfrac{1}{2}\times \dfrac{4\pi^2 r}{T^2}[/tex]
i.e. acceleration of ball becomes half. The correct option is (E).
(b) The acceleration of the ball in linear motion is given by :
[tex]a=\dfrac{v}{t}[/tex]
If the period halves and the speed halves, so the acceleration stays the same. The correct option is (A).
(c) Acceleration, [tex]a=\dfrac{4\pi^2 r}{T^2}[/tex]
If the period of rotation doubles and the radius stays the same, the acceleration is given by :
[tex]a'=\dfrac{4\pi^2 r}{(2T)^2}[/tex]
[tex]a'=\dfrac{a}{4}[/tex]
So, acceleration becomes quarters. The correct option is (D).
