(a) 
The relationship beween centripetal acceleration and angular speed is

where
is the angular speed
r is the radius of the circular path
Here we gave
is the centripetal acceleration
r = 5.15 m is the radius
Solving for
, we find:

(b) 21.3 m/s
The relationship between the linear speed and the angular speed is

where
v is the linear speed
is the angular speed
r is the radius of the circular path
In this problem we have

r = 5.15 m
Solving the equation for v, we find

No. It has no acceleration, which just means that the forces acting on it are equal and opposite, not that there are no forces exerted on it.
But if you're talking about the resulting Net Force, then yes you can conclude there is no Net Force acting on an object with no acceleration.
Via half-life equation we have:

Where the initial amount is 50 grams, half-life is 4 minutes, and time elapsed is 12 minutes. By plugging those values in we get:

There is 6.25 grams left of Ra-229 after 12 minutes.
(B) 1.00 m
Explanation:
Since the meter stick is traveling with Jill, it will have the same speed as she does so relative to Jill, the meter stick is stationary so its length remains 1.00 m as measured by her.
Answer:
In this scenario adding the dielectric material in between the plates will have no effect on the capacitance of the plates since the voltage remains unchanged
Explanation:
Normally Introducing a dielectric into a capacitor decreases the electric field, which decreases the voltage, which increases the capacitance.
A capacitor with a dielectric stores the same charge as one without a dielectric, but at a lower voltage.
Voltage and capacitance are inversely proportional when charge is constant.
Now in this case the voltage remains the same hence the charges remain the same also because voltage is inversely proportional to capacitance