Answer:
a)
, b)
, c)
,
, d) 
Explanation:
a) The gravitational force exerted by the Earth on the satellite is:



b) The centripetal acceleration of the satellite is:


c) The speed of the satellite is:



Likewise, the angular speed is:


d) The period of the satellite's rotation around the Earth is:


Answer:
Half life of the sample, 
Given:
Initial amount, N = 1679
Final count of amount, N' = 1336
Time elapsed, t = 4 min = 240 s
Solution:
Now, To calculate the half life, using the relation:

Now, substituting the given values in the above mentioned formula:


Taking log on both the sides:
ln(0.796) = \frac{4}{t_{\frac{1}{2}}}ln(0.5)


Answer:
The torque exerted on the merry-go-round is 766.95 Nm
Explanation:
Given;
mass of the merry-go-round, m = 416 kg
radius of the disk, r = 1.7 m
angular speed of the merry-go-round, ω = 3.7 rad/s
time of motion, t = 2.9 s
The torque exerted on the merry-go-round is calculated as;

Therefore, the torque exerted on the merry-go-round is 766.95 Nm