<u>Answer</u>: The potential difference across the resistor is 12 volts.
<u>Explanation:</u>
To calculate the potential difference cross the resistor, we use Ohm's Law. This law states that the potential difference across two wires is directly proportional to the current flowing through that wire.
Mathematically,

Where,
V = potential difference = ?V
I = Current flowing = 1.2 A
R = Resistor = 
Putting values in above equation, we get:

Hence, the potential difference across the resistor is 12 volts
Answer:
Part a)

Part b)

Part c)
distance L is independent of the mass of the sphere
Explanation:
Part a)
As we know that rotational kinetic energy of the sphere is given as

so we will have

so we will have




Part b)
By mechanical energy conservation law we know that
Work done against gravity = initial kinetic energy of the sphere
So we will have



Part c)
by equation of energy conservation we know that

so here we can see that distance L is independent of the mass of the sphere
This is a Fraunhofer single slit experiment, where the light passing through the slit produces an interference pattern on the screen, and where the dark bands (minima of diffraction) are located at a distance of

from the center of the pattern. In the formula, m is the order of the minimum,

the wavelenght,

the distance of the screen from the slit and

the width of the slit.
In our problem, the distance of the first-order band (m=1) is

. The distance of the screen is D=86 cm while the wavelength is

. Using these data and re-arranging the formula, we can find a, the width of the slit:
The frequency of a simple harmonic oscillator such as a spring-mass system is given by

where
k is the spring constant
m is the mass attached to the spring.
Re-arranging the formula, we get:

and since we know the constant of the spring:

and the frequency of oscillation:
f=1.00 Hz
we can find the value of the mass attached to it: