MCQ : Work And Energy - 1 - UPSC

One joule equals the work done ( or energy expended) by a force of One Newton (N) acting over a distance of one meter (m). One Newton equals a force that produces an acceleration of one meter per second (s) per second on a one Kilogram (Kg) mass. Therefore, one joule equals one Newton meter.

Given, the mass of the object m=100 kg, height h=5 m and g = - 10 ms^−2. ( Force is pulled upward acting opposite to gravity i.e g is negative)

Work done = potential energy

We know work done W=mgh

So, W = 50 × - 10 × 5 =  - 2500J

as force is perpendicular to displacement.

Given:
Mass of the Body (m) = 1 Kg.
Potential energy (E) = 1 Joule.
Acceleration Due to Gravity (g) = 9.8 m/s²
Explanation:
Potential Energy:-
Potential energy is the energy which a body posses due to virtue of Position.

Formula of Potential energy

P.E = Mgh

M denotes Mass of the Body.
g denotes Acceleration Due to Gravity.
h Denotes the Height to which the body is raisen.

From Potential energy Formula,

⇒ P.E = Mgh

⇒ E = M x g x h

⇒ E = 1 kg x 9.8 m/s² x h meters

⇒ E = 1 x 9.8 x h

⇒ E = 9.8 x h

∵ [ Potential Energy = 1 joule.]

Substituting,

⇒ 1 = 9.8 x h

⇒ h = 1/9.8

⇒ h = 10/98

⇒ h = 0.102 Meters.

So, The Height at which Potential Energy is 1 joule is 0.102 meters.

To determine where the energy of the bullet is lost, we need to consider the different forms of energy transfer involved.
1. Kinetic Energy: The bullet initially possesses kinetic energy as it moves towards the metal block.
2. Momentum Transfer: When the bullet collides with the metal block, it imparts momentum to the block.
3. Heat Energy: Some of the kinetic energy of the bullet is also converted into heat energy during the collision.
Given that the bullet stops on reaching 25 cm inside the metal block, we can conclude that the bullet loses all its kinetic energy and comes to rest. Therefore, the energy with the bullet is lost in both imparting momentum to the block and in the form of heat. Hence, the correct answer is option C: Both (a) and (b).
To summarize:
- The bullet loses its kinetic energy upon colliding with the metal block.
- The momentum of the bullet is transferred to the block, causing the block to move.
- Some of the kinetic energy is converted into heat energy during the collision.
Note: It is important to note that this solution assumes an idealized scenario where no other external factors, such as friction or air resistance, are present.

Explanation:

When a flying airplane is in motion, it possesses both potential and kinetic energy. Here's a detailed explanation of why it has both types of energy:
Potential Energy:
- Potential energy is the energy an object possesses due to its position or state.
- In the case of a flying airplane, it has potential energy due to its altitude or height from the ground.
- The higher the airplane is above the ground, the greater its potential energy.
Kinetic Energy:
- Kinetic energy is the energy an object possesses due to its motion.
- In the case of a flying airplane, it has kinetic energy due to its forward motion.
- The faster the airplane is moving, the greater its kinetic energy.
Combination of Potential and Kinetic Energy:
- As the airplane flies, it converts potential energy into kinetic energy and vice versa.
- When the airplane gains altitude, it increases its potential energy while decreasing its kinetic energy.
- When the airplane descends, it decreases its potential energy while increasing its kinetic energy.
- At any given moment during flight, the airplane has a combination of both potential and kinetic energy.
Conclusion:
- A flying airplane possesses both potential and kinetic energy simultaneously.
- Therefore, the correct answer is option C: both potential and kinetic energy.

Height will be upto the centre of gravity of tank, so P.E. =  mgh

Given:
Mass of particle 1 (m1) = 1 g = 0.001 kg
Mass of particle 2 (m2) = 4 g = 0.004 kg
Kinetic energy of both particles is equal.
We know that the kinetic energy of a particle is given by the formula:
Kinetic Energy = (1/2) * (mass of the particle) * (velocity of the particle)^2
Let the velocities of the two particles be v1 and v2 respectively.
Since the kinetic energy of both particles is equal, we have:
(1/2) * m1 * v1^2 = (1/2) * m2 * v2^2
Simplifying the equation:
m1 * v1^2 = m2 * v2^2
Taking the square root of both sides of the equation:
v1 = sqrt((m2 * v2^2) / m1)
The momentum of a particle is given by the formula:
Momentum = mass * velocity
Therefore, the momentum of particle 1 (p1) is given by:
p1 = m1 * v1
Similarly, the momentum of particle 2 (p2) is given by:
p2 = m2 * v2
To find the ratio between their momenta, we can divide the equation for p1 by the equation for p2:
(p1 / p2) = (m1 * v1) / (m2 * v2)
Substituting the value of v1 from the equation derived earlier:
(p1 / p2) = (m1 * sqrt((m2 * v2^2) / m1)) / (m2 * v2)
Simplifying the equation:
(p1 / p2) = sqrt((m1 / m2) * (v2 / v2))
Since v2 / v2 is equal to 1, we have:
(p1 / p2) = sqrt(m1 / m2)
Substituting the given values:
(p1 / p2) = sqrt(0.001 / 0.004)
Simplifying the equation:
(p1 / p2) = sqrt(1/4)
Taking the square root, we get:
(p1 / p2) = 1/2
Therefore, the ratio between the momenta of the two particles is 1 : 2.
Answer: C. 1 : 2

To determine the correct answer, we need to convert 1 kWh (kilowatt-hour) to joules.
1. Understand the conversion:
- 1 kilowatt-hour (kWh) is a unit of energy equal to 1 kilowatt (kW) of power used for 1 hour.
- To convert kWh to joules, we need to multiply the number of kilowatt-hours by the conversion factor.
2. Conversion factor:
- 1 kilowatt-hour (kWh) is equal to 3.6 x 10^6 joules.
- The conversion factor is derived from the relationship between kilowatts (kW) and joules (J).
3. Calculate the conversion:
- Multiply 1 kWh by the conversion factor of 3.6 x 10^6 joules/kWh.
- 1 kWh * 3.6 x 10^6 joules/kWh = 3.6 x 10^6 joules.
4. Compare the options:
- Option A: 3.6 x 10^6 joule - This matches the calculation above, so it is the correct answer.
- Option B: 3.6 x 10^3 joule - This is incorrect. The correct conversion factor is 3.6 x 10^6 joules.
- Option C: 3 x 19^8 joule - This is incorrect. The conversion factor does not involve the number 19.
- Option D: 300 joule - This is incorrect. The correct conversion is much larger than 300 joules.
Therefore, the correct answer is A: 3.6 x 10^6 joule.

We know, Power :- 
=  force * displacement/Time 
Force is 10 N, displacement = 6 m 
Time = 3 s 
Then, power = 10*6/3 => 10 * 2 ⇒ 20W