Answer: 8.81 J
Explanation: The scalar or dot product of 2 vector equals the product of the magnitude of both vectors and the cosine value of the angle between them
Magnitude of vector f (force) as given in the question = 12.5N
Magnitude of length = 0.75m
Angle between vectors = 25°
F. Δr = 12.5 * 0.75 * cos 25
F. Δr = 12.5 * 0.75 * 0.9063
F. Δr = 8.81 J
(a) 6.04 rev/s
The speed of the ball is given by:

where
is the angular speed
r is the distance of the ball from the centre of the circle
In situation 1), we have

r = 0.600 m
So the speed of the ball is

In situation 2), we have

r = 0.900 m
So the speed of the ball is

So, the ball has greater speed when rotating at 6.04 rev/s.
(b) 
The centripetal acceleration of the ball is given by

where
v is the speed
r is the distance of the ball from the centre of the trajectory
For situation 1),
v = 30.6 m/s
r = 0.600 m
So the centripetal acceleration is

(c) 
For situation 2 we have
v = 34.1 m/s
r = 0.900 m
So the centripetal acceleration is

Answer:
0.000025s
Explanation:
Period it’s. : T(s)= 1/f(Hz)=1/40000Hz=0.000025s
The initial force between the two charges is given by:

where k is the Coulomb's constant, q1 and q2 the two charges, d their separation. Let's analyze now the other situations:
1. F
In this case, q1 is halved, q2 is doubled, but the distance between the charges remains d.
So, we have:

So, the new force is:

So the force has not changed.
2. F/4
In this case, q1 and q2 are unchanged. The distance between the charges is doubled to 2d.
So, we have:

So, the new force is:

So the force has decreased by a factor 4.
3. 6F
In this case, q1 is doubled and q2 is tripled. The distance between the charges remains d.
So, we have:

So, the new force is:

So the force has increased by a factor 6.