Answer: 
Explanation:
Given
Length of beam 
mass of beam 
Two forces of equal intensity acted in the opposite direction, therefore, they create a torque of magnitude

Also, the beam starts rotating about its center
So, the moment of inertia of the beam is

Torque is the product of moment of inertia and angular acceleration

Answer: An 8 kg book at a height of 3 m has the most gravitational potential energy.
Explanation:
Gravitational potential energy is the product of mass of object, height of object and gravitational field.
So, formula to calculate gravitational potential energy is as follows.
U = mgh
where,
m = mass of object
g = gravitational field = 
h = height of object
(A) m = 5 kg and h = 2m
Therefore, its gravitational potential energy is calculated as follows.

(B) m = 8 kg and h = 2 m
Therefore, its gravitational potential energy is calculated as follows.

(C) m = 8 kg and h = 3 m
Therefore, its gravitational potential energy is calculated as follows.

(D) m = 5 kg and h = 3 m
Therefore, its gravitational potential energy is calculated as follows.

Thus, we can conclude that an 8 kg book at a height of 3 m has the most gravitational potential energy.
This is an interesting (read tricky!) variation of Rydberg Eqn calculation.
Rydberg Eqn: 1/λ = R [1/n1^2 - 1/n2^2]
Where λ is the wavelength of the light; 1282.17 nm = 1282.17×10^-9 m
R is the Rydberg constant: R = 1.09737×10^7 m-1
n2 = 5 (emission)
Hence 1/(1282.17 ×10^-9) = 1.09737× 10^7 [1/n1^2 – 1/25^2]
Some rearranging and collecting up terms:
1 = (1282.17 ×10^-9) (1.09737× 10^7)[1/n2 -1/25]
1= 14.07[1/n^2 – 1/25]
1 =14.07/n^2 – (14.07/25)
14.07n^2 = 1 + 0.5628
n = √(14.07/1.5628) = 3