Cost of electrical energy MCQs for Grade 9 Exam

Understanding Energy Consumption
To calculate the energy consumed by a 60-watt bulb used for 6 hours a day, we first need to understand the concept of watts, which is a unit of power.
Step 1: Calculate Daily Energy Consumption
- The formula to calculate energy consumption in kilowatt-hours (kWh) is:
- Energy (kWh) = Power (kW) × Time (h)
- Convert watts to kilowatts:
- 60 watts = 0.06 kW
Step 2: Substitute Values
- Using the formula:
- Energy (kWh) = 0.06 kW × 6 h
Step 3: Perform the Calculation
- Multiply the values:
- Energy (kWh) = 0.36 kWh
Step 4: Convert to Units
- In the context of electricity, 1 unit is equivalent to 1 kWh.
- Therefore, the energy consumed by the bulb in one day is 0.36 units.
Conclusion
- The correct answer is option 'B' - 0.36 units.
- This means that using a 60-watt bulb for 6 hours will consume 0.36 units of energy per day.
This calculation helps in understanding how much energy different appliances use, which is essential for managing electricity costs effectively.

Remains the same

At highest point, velocity is zero.

The type of energy possessed by a simple pendulum, when it is at the mean position, is kinetic energy (K.E).

Explanation:

A simple pendulum consists of a mass (bob) attached to a string or rod that is fixed at one end. When the pendulum is at the mean position, it is at its lowest point and has the highest potential energy. As it swings away from the mean position, the potential energy is converted into kinetic energy, and vice versa.

Understanding the options:

To determine the type of energy possessed by a simple pendulum at the mean position, let's analyze each option:

a) K.E (Kinetic Energy): Kinetic energy is the energy possessed by an object due to its motion. In the case of a simple pendulum, when it is at the mean position, it momentarily comes to rest before changing direction. At this point, it has no potential energy but possesses kinetic energy due to its motion. Therefore, option 'A' is correct.

b) P.E (Potential Energy): Potential energy is the energy possessed by an object due to its position or state. When the pendulum is at the mean position, it is at its lowest point and has the highest potential energy. However, at this point, it does not possess potential energy but has kinetic energy instead.

c) K.E + P.E (Kinetic Energy + Potential Energy): This option suggests that the pendulum possesses both kinetic and potential energy simultaneously at the mean position. However, as explained earlier, the pendulum only has kinetic energy at this point.

d) Sound Energy: Sound energy is the energy produced by the vibrations of particles in a medium. When the simple pendulum is at the mean position, it is not producing any sound energy.

Conclusion:

Based on the analysis, the correct answer is option 'A' - Kinetic Energy (K.E). The simple pendulum possesses kinetic energy at the mean position.

Given:
Mass of the bag, m = 50 kg
Height of the coolie, h = 200 cm = 2 m
Acceleration due to gravity, g = 10 m/s^2

To Find:
The work done by the coolie in lifting the bag.

Solution:
The work done (W) is given by the formula:

W = mgh

where,
m = mass of the object (in kg)
g = acceleration due to gravity (in m/s^2)
h = height (in meters)

Substituting the given values:
m = 50 kg
g = 10 m/s^2
h = 2 m

W = (50 kg) * (10 m/s^2) * (2 m)
W = 1000 J

Hence, the work done by the coolie in lifting the bag is 1000 J.

Explanation:
- The work done in lifting an object is equal to the product of the force applied and the distance over which the force is applied.
- In this case, the coolie is applying a force to lift the bag against the force of gravity.
- The force applied by the coolie is equal to the weight of the bag, which is given by the formula: F = mg, where m is the mass of the bag and g is the acceleration due to gravity.
- The distance over which the force is applied is the height to which the bag is lifted.
- Therefore, the work done by the coolie is equal to the weight of the bag multiplied by the height to which it is lifted.
- Substituting the given values into the formula, we can calculate the work done as 1000 J.
- Hence, the correct answer is option B, 1000 J.

Explanation:

Introduction:
Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass and velocity of the object. The formula for kinetic energy is given by:

Kinetic energy (KE) = 0.5 * mass * velocity^2

Effect of doubling the speed:
When the speed of an object is doubled, it means that the new velocity becomes twice the original velocity. Let's assume the initial velocity is 'v' and the final velocity (after doubling) is '2v'.

Comparing the kinetic energy:
To determine the effect on kinetic energy, we can compare the kinetic energy before and after doubling the speed.

Initial kinetic energy:
Using the formula for kinetic energy, the initial kinetic energy can be calculated as:
KE1 = 0.5 * mass * v^2

Final kinetic energy:
After doubling the speed, the final kinetic energy can be calculated as:
KE2 = 0.5 * mass * (2v)^2 = 0.5 * mass * 4v^2

Comparing KE1 and KE2:
Let's compare the initial and final kinetic energies:
KE2 / KE1 = (0.5 * mass * 4v^2) / (0.5 * mass * v^2)
= (2 * mass * v^2) / (0.5 * mass * v^2)
= 4

Therefore, the final kinetic energy (KE2) is four times the initial kinetic energy (KE1) when the speed is doubled.

Conclusion:
Hence, the correct answer is option 'C' - Quadrupled. When the speed of an object is doubled, its kinetic energy increases by a factor of four.

To find the work done in pulling the toy car, we need to use the formula for work done:

Work = Force × Distance × cos(angle)

Given:
Force = 15 N
Angle = 60°
Distance = 20 m

Let's calculate the work done step by step:

1. Calculate the value of cos(60°):
cos(60°) = 0.5

2. Substitute the given values into the formula for work:
Work = 15 N × 20 m × 0.5

3. Simplify the expression:
Work = 300 Nm × 0.5
Work = 150 J

Therefore, the work done in pulling the toy car by a distance of 20 meters is 150 Joules (J).

So, the correct answer is option A) 150 J.

Explanation:

When a stone is tied to a string and whirled in a circle, the work done by the string is zero. This is because work is defined as the product of force and displacement in the direction of the force. In this case, the force exerted by the string on the stone is always perpendicular to the displacement of the stone.

Work Done:
The work done by a force can be calculated using the formula:

Work = Force x Displacement x cosθ

Where:
- Force is the magnitude of the force applied.
- Displacement is the magnitude of the displacement.
- θ is the angle between the force and displacement vectors.

In this case, the force exerted by the string on the stone is always perpendicular to the displacement of the stone. Therefore, the angle θ between the force and displacement vectors is 90 degrees, and cosθ = 0.

Work Done by the String:
When cosθ = 0, the work done by the force is zero. This means that the work done by the string on the stone is zero. The string does not contribute any work to the motion of the stone.

Reasoning:
The reason behind the zero work done is that the force exerted by the string is always perpendicular to the displacement of the stone. As a result, the force and displacement vectors are always at right angles to each other, and the angle between them is 90 degrees. When the angle between the force and displacement vectors is 90 degrees, the work done by the force is zero.

Conclusion:
In conclusion, when a stone is tied to a string and whirled in a circle, the work done by the string is zero. This is because the force exerted by the string is always perpendicular to the displacement of the stone, resulting in a zero angle between the force and displacement vectors. Thus, the correct answer is option 'C' - Zero.

Potential and Kinetic Energies of a Freely Falling Body

When air resistance is negligible, the sum total of potential and kinetic energies of a freely falling body remains the same.

Explanation:

1. Potential Energy:
Potential energy is the energy possessed by an object due to its position or state. In the case of a freely falling body, the potential energy is gravitational potential energy, which is given by the formula:

PE = mgh

Where:
- PE is the potential energy
- m is the mass of the object
- g is the acceleration due to gravity
- h is the height of the object above a reference point

As the object falls, its height decreases, resulting in a decrease in potential energy.

2. Kinetic Energy:
Kinetic energy is the energy possessed by an object due to its motion. In the case of a freely falling body, the kinetic energy is given by the formula:

KE = 0.5mv^2

Where:
- KE is the kinetic energy
- m is the mass of the object
- v is the velocity of the object

As the object falls, its velocity increases due to the acceleration due to gravity. Therefore, the kinetic energy increases.

3. Sum Total of Potential and Kinetic Energies:
The sum total of potential and kinetic energies is given by the equation:

Total Energy = Potential Energy + Kinetic Energy

As the object falls, the potential energy decreases, but the kinetic energy increases. However, the decrease in potential energy is exactly equal to the increase in kinetic energy. This means that the sum total of potential and kinetic energies remains constant throughout the fall.

Conclusion:
In the absence of air resistance, the sum total of potential and kinetic energies of a freely falling body remains the same. This is because the decrease in potential energy is exactly balanced by the increase in kinetic energy.

Explanation:
When a body is at a certain height, it possesses potential energy due to its position in the Earth's gravitational field. The potential energy (P.E.) possessed by the body is given as 200 J.

Step 1: Understanding Potential Energy and Kinetic Energy
Potential energy (P.E.) is the energy possessed by an object due to its position or state. It is the energy that can be converted into other forms of energy. In the case of a body at a height, the potential energy is due to its position in the Earth's gravitational field.

Kinetic energy (K.E.) is the energy possessed by an object due to its motion. It depends on the mass of the object and its velocity.

Step 2: Relationship between Potential Energy and Kinetic Energy
When the body just touches the surface of the Earth, it means that it has fallen from a height and its potential energy has been completely converted into kinetic energy. At this point, the body has no potential energy left.

According to the law of conservation of energy, energy cannot be created or destroyed, only transferred or converted from one form to another. Therefore, the potential energy possessed by the body at the height must be equal to the kinetic energy it possesses when it touches the surface of the Earth.

Step 3: Determining the Kinetic Energy
Since the potential energy of the body is given as 200 J, this must be equal to the kinetic energy when it touches the surface of the Earth.

Therefore, the K.E. possessed by the body when it just touches the surface of the Earth is also 200 J.

Step 4: Conclusion
Therefore, the correct answer is option C: 200 J. The K.E. possessed by the body when it just touches the surface of the Earth is equal to the potential energy it had at the height, which is 200 J.

Understanding Momentum and Kinetic Energy
To solve for the kinetic energy of the bullet, we first need to understand the relationship between momentum and kinetic energy.
Definitions
- Momentum (p): It is defined as the product of mass (m) and velocity (v) of an object.
- Formula: p = m * v
- Kinetic Energy (KE): It is defined as the energy that an object possesses due to its motion.
- Formula: KE = (1/2) * m * v^2
Given Information
- Mass of the bullet (m): 20 g = 0.020 kg (conversion to kg)
- Momentum (p): 10 kg·m/s
Finding Velocity
Using the momentum formula:
- p = m * v
- Rearranging gives us: v = p / m
- Substituting the values:
- v = 10 kg·m/s / 0.020 kg = 500 m/s
Calculating Kinetic Energy
Now that we have the velocity, we can find the kinetic energy:
- KE = (1/2) * m * v^2
- KE = (1/2) * 0.020 kg * (500 m/s)^2
- KE = 0.010 kg * 250000 m²/s²
- KE = 2500 J
Converting to kJ
Since 1 kJ = 1000 J:
- KE = 2500 J = 2.5 kJ
Conclusion
The kinetic energy of the bullet is 2.5 kJ, thus confirming that option 'C' is correct.

When the displacement of the body is

Kinetic energy into heat energy

K.E. = ½ mv² = ½ × (250/1000) × (10)² = 12.5 J

To find the energy possessed by the ball, we need to calculate its kinetic energy. Kinetic energy is given by the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Given data:
Mass of the ball = 550g = 0.55kg
Velocity of the ball = 25 m/sec

Let's calculate the kinetic energy step by step.

1. Convert the mass to kilograms:
Mass of the ball = 0.55kg

2. Calculate the kinetic energy using the formula:
Kinetic Energy = (1/2) * 0.55kg * (25 m/sec)^2

3. Simplify the equation:
Kinetic Energy = (1/2) * 0.55kg * 625 m^2/sec^2
Kinetic Energy = 0.275kg * 625 m^2/sec^2
Kinetic Energy = 171.875 J

Therefore, the energy possessed by the ball of mass 550g rolling on the surface with a speed of 25 m/sec is 171.875 Joules (J).

So, the correct answer is option C) 171.875 J.