Worksheet with Solutions: Work, Power and Energy | Physics Class 11 - NEET PDF Download

Ans: a) Joule
The SI unit of work is the Joule, which is defined as the work done when a force of one newton displaces an object by one meter in the direction of the force.

​Ans: c) Work
Work is a scalar quantity, representing the amount of energy transferred when a force moves an object over a distance, without a direction associated.

Ans: c) Zero
The work done is zero when the force is perpendicular to the displacement, as no energy is transferred in the direction of the force.

Ans: c) The change in kinetic energy
The work-energy theorem states that the work done on an object is equal to its change in kinetic energy, reflecting the relationship between work and energy.

Ans: b) PE = mgh
The formula for gravitational potential energy is PE = mgh, where m is mass, g is the acceleration due to gravity, and h is height above a reference point.

Ans: displacement
The work done by a force is calculated as the product of the force and the displacement in the direction of the force. This relationship is crucial in understanding how forces perform work.

Ans: watt
Power is defined as the rate at which work is done or energy is transferred. The standard unit of power is the watt, representing one joule per second.

Ans: kinetic
The energy associated with the motion of an object is termed kinetic energy. It is represented mathematically by the formula K = 1/2 mv², where m is mass and v is velocity.

Ans: thermal
When work is performed against friction, the mechanical energy is transformed into thermal energy, which is typically experienced as heat.

Ans: energy
The principle known as the law of conservation of energy asserts that within a closed system, energy can neither be created nor annihilated, only changed from one form to another.

Ans: True
Work is defined as the product of force and displacement in the direction of that force, meaning it requires both a force and a movement in that direction for work to be done.

Ans: False
Power is a scalar quantity that measures the rate at which work is done or energy is transferred, and it does not have a direction.

Ans: True
Negative work occurs when the force applied to an object is in the opposite direction of the object's displacement, resulting in a decrease in kinetic energy.

Ans: False
Kinetic energy is directly proportional to the square of an object’s speed; therefore, as speed decreases, kinetic energy also decreases.

Ans: True
Potential energy is indeed energy that is stored based on an object's position relative to other forces, such as gravitational potential energy based on height.

Sol: 

Ans: Work in physics refers to the process of applying a force to move an object over a certain distance. It is calculated using the formula:

• Work = Force × Distance

Here, force is the push or pull applied to the object, and distance is how far the object moves in the same direction as the force.

Ans: Energy is the ability to do work. When work is done on an object, energy is transferred to it, causing the object to move or change form.

Ans: The formula for kinetic energy is K = 1/2 mv², where m is the mass of the object and v is its speed. This means that if you know how heavy something is and how fast it is moving, you can calculate its energy.

Ans: Potential energy is the energy that is stored in an object due to its position or condition. For instance, a ball that is held high above the ground possesses potential energy because it has the ability to fall down.

Ans: Power refers to the rate at which work is performed. It quantifies the amount of work done over a specified period of time. The formula for calculating power is:

• Power = Work / Time

This means that power indicates how quickly energy is transferred or converted in a system.

Ans: In physics, the concepts of work, energy, and power are fundamental to understanding how forces affect motion and how energy is transferred or transformed. Here’s a detailed explanation of each concept and their interrelationships:

• Work: Work is defined as the product of the force applied to an object and the displacement of that object in the direction of the force. Mathematically, work (W) can be expressed as: W = F × d × cos(θ) where F is the magnitude of the force, d is the displacement, and θ is the angle between the direction of the force and the direction of the displacement. Work is measured in joules (J). If the force and displacement are in the same direction, work is positive; if they are in opposite directions, work is negative.
• Energy: Energy is the capacity to perform work. There are various forms of energy, including kinetic energy (energy of motion) and potential energy (stored energy). The kinetic energy (K.E.) of an object is given by the formula: K.E. = (1/2) mv² where m is the mass of the object and v is its velocity. Potential energy (P.E.), particularly gravitational potential energy, is given by: P.E. = mgh where h is the height above a reference point. Energy is also measured in joules (J).
• Power: Power is defined as the rate at which work is done or energy is transferred. It can be mathematically represented as: P = W/t where P is power, W is work, and t is the time taken to do the work. Power is measured in w Watts (W), where 1 watt equals 1 joule per second (1 W = 1 J/s).
• Interrelation: The relationship between work, energy, and power is encapsulated in the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. This can be expressed as: ΔK.E. = W This shows that when work is done on an object, it either increases or decreases its kinetic energy. Moreover, power measures how quickly this work is done, highlighting the efficiency of energy transfer in a given time.
• Examples: A simple example is lifting a weight. When you lift a 10 kg weight to a height of 2 meters, you do work against gravity. The gravitational force (F = mg = 10 kg × 9.81 m/s²) acts downward, and as you lift the weight, the height (h) increases, converting work into potential energy. The power exerted can be calculated by measuring how fast you lift the weight. If you lift it in 2 seconds, the power is the total work done divided by the time.

Ans: The work-energy theorem is a fundamental principle in physics that connects the work done on an object to its change in kinetic energy. The theorem states that the total work done by all forces acting on an object equals the change in its kinetic energy, which can be expressed mathematically as: ΔK.E. = W where ΔK.E. is the change in kinetic energy and W is the total work done on the object.

• Constant Forces: When a constant force acts on an object, the work done can be calculated easily. For instance, if a 5 N force is applied to push a box 4 meters along a surface, the work done is:
• W = F × d = 5 N × 4 m = 20 J This work results in a corresponding change in the kinetic energy of the box, assuming it starts from rest. If the initial kinetic energy is zero, the final kinetic energy becomes 20 J.
• Variable Forces: For cases where the force varies, calculating work involves integration. For example, consider a spring that follows Hooke's law, where the force exerted by the spring is proportional to its displacement (F = kx). The work done in stretching or compressing the spring can be calculated by integrating the force over the displacement:
• W = ∫ F dx = ∫ kx dx from 0 to x This integral results in the potential energy stored in the spring, demonstrating how variable forces can be handled using calculus.
• Practical Application: The work-energy theorem is widely applied in various fields, including engineering and biomechanics. For instance, when analysing the motion of vehicles, understanding how the work done by engine forces (overcoming friction and air resistance) translates into changes in kinetic energy helps in optimising performance and fuel efficiency.
• Example of a Falling Object: Consider a raindrop falling under the influence of gravity. As it falls, gravitational force does work on it, converting potential energy into kinetic energy. If it starts from rest and falls from a height of 100 m, using the work-energy theorem, we can determine its velocity just before impact.
• Conclusion: The work-energy theorem provides a powerful framework for analysing the effects of forces on an object's motion. Whether dealing with constant forces, like pushing a box, or variable forces, like a spring, this theorem applies universally in physics, allowing us to connect work, energy, and motion.

Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
A conservative force (like gravity or spring force) has the property that the work done depends only on the initial and final positions, not on the actual path taken — that is, it’s path-independent.
Moreover, if the path is a closed loop (i.e., the object returns to its starting point), then the net work done by the conservative force is zero.
This zero work over a closed loop directly implies path-independence, so R correctly explains A.

Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
The spring force follows Hooke’s Law: F = −kx.
When a block is attached to a spring and moved from one position to another, the work done by the spring force depends only on the initial and final displacement (not the actual path), as shown by the expression:

Hence, the spring force is conservative, and since the work depends only on positions, R correctly explains A.

Answer: (d) A is false but R is true.
Explanation:
In an inelastic collision, some kinetic energy is converted to other forms like heat, sound, or deformation. So, total kinetic energy is not conserved.
However, total linear momentum is always conserved in a collision (elastic or inelastic), as long as no external force acts on the system.
Thus, A is false, but R is true.

Ans: Given:

• Mass of block = 1 kg

• Initial velocity = 2 m/s

• Initial kinetic energy (K.E.) = (1/2) × 1 × (2)² = 2 joules

• Retarding force = -0.5 / x (from x = 0.1 m to x = 2.01 m)

Work done by the force is:
W = ∫ from 0.1 to 2.01 of (-0.5 / x) dx
This gives:
W = -0.5 × ln(2.01 / 0.1)
= -0.5 × ln(20.1)
≈ -0.5 × 3
= -1.5 joules

According to the Work-Energy Theorem,
Final K.E. = Initial K.E. + Work done
Final K.E. = 2 + (-1.5) = 0.5 joules

​Ans: Given:

• Mass of bullet = 50 g = 0.05 kg

• Initial speed = 200 m/s

• Final kinetic energy is 10% of the initial kinetic energy
  We are asked to find the final speed of the bullet.

Initial K.E. = (1/2) × mass × (initial speed)²
= (1/2) × 0.05 × (200)²
= 0.025 × 40000
= 1000 joules

Since the bullet retains only 10% of its initial K.E.:
Final K.E. = 10% of 1000 = 100 joules

We use the kinetic energy formula again to find final speed (v):
100 = (1/2) × 0.05 × v²
⇒ 100 = 0.025 × v²
⇒ v² = 100 / 0.025 = 4000
⇒ v = √4000 = 63.2 m/s (approximately)