To establish the age of a rock or a fossil, researchers use some type of clock to determine the date it was formed. Geologists commonly use radiometric dating methods, based on the natural radioactive decay of certain elements such as potassium and carbon, as reliable clocks to date ancient events.
To solve this problem we will use the concepts related to Torque as a function of the Force in proportion to the radius to which it is applied. In turn, we will use the concepts of energy expressed as Work, and which is described as the Torque's rate of change in proportion to angular displacement:

Where,
F = Force
r = Radius
Replacing we have that,



The moment of inertia is given by 2.5kg of the weight in hand by the distance squared to the joint of the body of 24 cm, therefore


Finally, angular acceleration is a result of the expression of torque by inertia, therefore



PART B)
The work done is equivalent to the torque applied by the distance traveled by 60 °° in radians
, therefore



Answer:
the final speed of object A changed by a factor of
= 0.58
the final speed of object B changed by a factor of
= 1.29
Explanation:
Given;
kinetic energy of object A, = 27 J
let the mass of object A = 
then, the mass of object B = 
work done on object A = -18 J
work done on object B = -18 J
let
be the initial speed
let
be the final speed
For object A;


Thus, the final speed of object A changed by a factor of
= 0.58
To obtain the change in the final speed of object B, apply the following equations.


Thus, the final speed of object B changed by a factor of
= 1.29
Answer:
The wavelength in vacuum is equal to 428.8 nm.
Explanation:
Given that,
The wavelength of light, 
The refractive index of glass, n = 1.51
We need to find the wavelength in vacuum. The relation between wavelength and refractive index is given by :

So, the wavelength in vacuum is equal to 428.8 nm.