Certainly! Let's address each part of the question one by one.
### Part 1: Defining Power
Power is defined as the rate at which work is done or energy is transferred over time. The formula for power ([tex]\(P\)[/tex]) can be represented as:
[tex]\[ P = \frac{W}{t} \][/tex]
where:
- [tex]\( P \)[/tex] is the power,
- [tex]\( W \)[/tex] is the work done or energy transferred (usually in joules),
- [tex]\( t \)[/tex] is the time taken (usually in seconds).
### Part 2: Cost to Operate a Lamp
Question: Find the cost of running a 60-watt lamp for 24 hours if 1 kWh costs [tex]$5.
1. First, we calculate the energy consumption of a 60-watt lamp running for 24 hours.
\[
\text{Energy consumption} = \text{Power} \times \text{Time}
\]
Converting power to kilowatts:
\[
\text{Power} = 60 \text{ watts} = 0.06 \text{ kW}
\]
\[
\text{Time} = 24 \text{ hours}
\]
\[
\text{Energy consumption} = 0.06 \text{ kW} \times 24 \text{ hours} = 1.44 \text{ kWh}
\]
2. Next, calculate the cost:
\[
\text{Cost} = \text{Energy consumption} \times \text{Cost per kWh}
\]
\[
\text{Cost} = 1.44 \text{ kWh} \times 5 = \$[/tex]7.20
\]
### Part 3: Defining Young's Modulus of Elasticity
Young's Modulus of Elasticity ([tex]\(E\)[/tex]) is a measure of the stiffness of a solid material. It is defined as the ratio of tensile stress ([tex]\(\sigma\)[/tex]) to tensile strain ([tex]\(\varepsilon\)[/tex]):
[tex]\[ E = \frac{\sigma}{\varepsilon} \][/tex]
where:
- [tex]\(\sigma\)[/tex] is the tensile stress (force per unit area),
- [tex]\(\varepsilon\)[/tex] is the tensile strain (proportional deformation in length).
### Part 4: Work Done by the Load on a Wire
Question: A wire of length 55 m and force constant [tex]\(700 \,\text{N/m}\)[/tex] extends to 55.00 m when loaded. Calculate the work done by the load.
1. Calculate the extension of the wire:
[tex]\[
\Delta L = 55.00 \, \text{m} - 55 \, \text{m} = 0.00 \, \text{m}
\][/tex]
2. The work done [tex]\(W\)[/tex] by the load on the wire is calculated using Hooke’s Law:
[tex]\[
W = \frac{1}{2}k (\Delta L)^2
\][/tex]
where [tex]\(k\)[/tex] is the force constant of the wire (700 N/m).
[tex]\[
W = \frac{1}{2} \times 700 \times (0.00)^2 = 0 \text{ J}
\][/tex]
### Part 5: Moment of a Force
a) Defining the Moment of a Force:
The moment of a force (or torque) is the measure of its tendency to cause a body to rotate about a specific point or axis. It is calculated as the product of the force ([tex]\(F\)[/tex]) and the distance ([tex]\(d\)[/tex]) from the point to where the force is applied:
[tex]\[ \text{Moment} = F \times d \][/tex]
### Part 6: Conditions for Stability
b) Two conditions necessary for the stability of a body:
1. The center of gravity should be as low as possible to minimize the chance of toppling.
2. The base of support should be wide enough to prevent tipping over in response to external forces.
### Part 7: First Law of Reflection
Law: The first law of reflection states that the angle of incidence is equal to the angle of reflection. These angles are measured relative to the normal at the point of incidence on the reflective surface.
### Part 8: Number of Images Formed by Mirrors
Question: The mirrors are inclined at an angle [tex]\(60^{\circ}\)[/tex] to each other. Calculate the number of images formed.
When two mirrors are inclined at an angle [tex]\(\theta\)[/tex] to each other, the number of images ([tex]\(N\)[/tex]) formed can be calculated using the formula:
[tex]\[
N = \frac{360^\circ}{\theta} - 1
\][/tex]
For [tex]\(\theta = 60^\circ\)[/tex]:
[tex]\[
N = \frac{360^\circ}{60^\circ} - 1 = 6 - 1 = 5
\][/tex]
Thus, 5 images are formed.
