Lakhmir Singh & Manjit Kaur Test: Work Energy - Free MCQ with solutions

First, we determine the mass of the body using F = ma:
25 N = m × 5 m/s² → m = 5 kg.

Since the body starts from rest and accelerates at 5 m/s² for 2 seconds, its final velocity is:
v = u + at = 0 + (5)(2) = 10 m/s.

Hence, the kinetic energy acquired is:
K = 1/2 mv² = 1/2 × 5 × (10)² = 250 J.

Thus, the correct answer is 250 J.

- A freely falling body is influenced by gravity, which causes it to accelerate downwards.
- Kinetic Energy: As the body falls, its velocity increases, resulting in an increase in kinetic energy.
- Potential Energy: Initially, when the body is at a height, it possesses potential energy due to its position.
- As it falls, potential energy decreases while kinetic energy increases, conserving the total mechanical energy.
- Thus, during the fall, the body has both kinetic and potential energy.

The formula for gravitational potential energy is:
P.E. = mgh

Where:

m = mass of the boy

g = acceleration due to gravity (9.8 m/s²)

h = height of the wall (3.4 m)

Given:
P.E. = 2250 J, g = 9.8 m/s², h = 3.4 m

Substitute the given values into the formula and solve for m:
2250 = m × 9.8 × 3.4

Calculate the product 9.8 × 3.4:
9.8 × 3.4 = 33.32

Thus,
2250 = m × 33.32

Divide both sides by 33.32 to find m:
m = 2250 / 33.32 ≈ 67.5 kg

Step 1: Mass m = 4 kg,
            Momentum p = 25 kg·m/s

Step 2: From p = m × v
            → 25 = 4 × v
            → v = 25/4 = 6.25 m/s
Step 3: Kinetic energy KE = 1/2 m v² = 1/2 × 4 × (6.25)² = 2 × 39.0625 = 78.125 J
Answer: 78.125 J → option (b)

Let the mass be m, and velocity v.
Then,

Kinetic Energy = 1/2 × m × v².

When 3/4th of its mass is removed,
Mass of the new body = m - (3/4) × m = 1/4 × m.

When velocity is doubled,
New velocity will be 2v.

Then,
New Kinetic Energy = 1/2 × (1/4 × m) × (2v)².

New Kinetic Energy = 1/2 × m × v².

Thus, Kinetic Energy = New Kinetic Energy.

Hence, Kinetic Energy will not change when 3/4th of its mass is removed and velocity is doubled.

Potential energy is the energy stored in an object due to its position. Raising a body to a height increases its gravitational potential energy, as energy is stored due to its elevated position in a gravitational field. Setting it into motion involves kinetic energy, not potential energy. Using an elastic band stores elastic potential energy in the band, not the body. Destroying the body does not store energy; it disperses it. Therefore, the correct answer is D: Raising the body to a height.

Kinetic Energy = (¹/₂) mv².

If the velocity of a body is halved, its kinetic energy becomes one fourth as kinetic energy is directly proportional to velocity squared.

To find the height through which the fish dived, use the concept of gravitational potential energy and kinetic energy.

• The weight of the fish is 35 kg.
• The kinetic energy when hitting the ground is 3500 J.
• Gravitational potential energy at the height is converted to kinetic energy at the ground.

Use the formula for gravitational potential energy:

• Potential Energy = Mass × Gravity × Height
• 3500 J = 35 kg × 10 m/s² × Height

Solving for Height:

• Height = 3500 / (35 × 10) = 10 m

Therefore, the height is 10 metres.

The correct option is D.
A moving car is an example of kinetic energy whereas water stored in a dam, compressed spring and stretched rubber band are examples of potential energy.

K.E = 0.5mv²
v = √(2K.E / m)
= √(2 × 625 Joule / 50 kg)
= √(625 Joule / 25 kg)
= 5 m/s...

According to the Work-Energy Theorem, the work done is equal to the change in kinetic energy. Therefore:

• Work done = final KE - initial KE
• final KE = 60 J
• initial KE = 12 J
• Work done = 60 J - 12 J = 48 J

since kinetic energies are equal

KE₁ = KE₂

mv₁²/2 = 4mv₂²/2

v₁/v₂ = √4/1 = 2:1

The formula for kinetic energy (KE) is:
KE = 1/2 × m × v²

Where:

• m is the mass of the object,
• v is the velocity of the object.

If the speed (v) of the object doubles, then:
v_new = 2v

The new kinetic energy becomes:
KE_new = 1/2 × m × (2v)²
KE_new = 1/2 × m × 4v²
KE_new = 4 × (1/2 × m × v²)

Thus, the new kinetic energy is 4 times the original kinetic energy.

KE = K = 1 /2( mv²) 
We know, p = mv
⇒ K = p² / 2m
 p²  =  2Km
Because K is constant, we see:
p is proportional to the square root of m.
Therefore, the correct relationship is:
p ∝ √m.

As, KE is Same, ie . Constant, momentum would be directly proportional to the square root of mass.

1 joule (J) is defined as the amount of work done when a force of 1 newton (N) moves an object by 1 metre (m) in the direction of the force. The unit of work (and energy) is the newton-metre, which is also called a joule. Therefore, 1 joule is the energy required to do 1 newton-metre (1 N·m) of work. So, option c) 1 N·m is correct.

Work-Energy Theorem:

W_net = ΔK = K_final - K_initial

Initial kinetic energy (when v = 10 m/s):
K_initial = 1/2 × m × v² = 1/2 × 44 kg × (10 m/s)² = 1/2 × 44 × 100 = 2200 J

Final kinetic energy (at rest, v = 0):
K_final = 1/2 × m × (0)² = 0

Hence, the change in kinetic energy is:
ΔK = 0 - 2200 J = -2200 J

Conclusion:
The net work done on the body (by the force that brings it to rest) is -2200 J.
The negative sign indicates that the work done on the body is opposing its motion, reducing its kinetic energy to zero.

- Gravitational potential energy depends on an object's position relative to a reference point, typically the ground.
- An object has gravitational potential energy when it is at an elevated position, as energy is stored due to its height in a gravitational field.
- Options like accelerating, moving, or falling involve kinetic energy or changes in energy types.
- Thus, for an object to have gravitational potential energy only, it must be at an elevated position with respect to the ground.

In physics the Kinetic energy (KE) of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. 

Potential energy is the energy that is stored in an object due to its position relative to some zero position. 

The correct answer is C: Ocean thermal energy.

• Ocean Thermal Energy Conversion (OTEC) utilizes the temperature difference between warmer surface water and colder deep water to generate electricity.
• This temperature gradient drives a heat engine, producing energy