Work, Energy and Simple Machines: NCERT Solutions (2026)

Work is said to be done in science when two specific conditions are satisfied:

1. A force must act on the object.
2. The object must be displaced from its initial position in the direction of the applied force.

The kinetic energy (\(E_k\)) of an object of mass \(m\) moving with a velocity \(v\) is given by the expression:

$$E_k = \frac{1}{2}mv^2$$

Power: It is defined as the rate of doing work or the rate at which energy is consumed. Formula: \(P = \frac{W}{t}\)

1 Watt: Power is said to be 1 watt when 1 Joule of work is done in 1 second. (\(1 \text{ W} = 1 \text{ J/s}\)).

Given:
Work done / Energy consumed (\(W\)) = 1000 J
Time taken (\(t\)) = 10 s

Formula:
$$P = \frac{W}{t}$$ $$P = \frac{1000}{10}$$ $$P = 100 \text{ W}$$

The power of the lamp is 100 Watts.

Step 1: The minimum force required to raise the object is equal to the weight of the object. Therefore, Force (\(F\)) = \(mg\).

Step 2: The displacement of the object is the height it is raised to. Therefore, Displacement (\(s\)) = \(h\).

Step 3: Work done (\(W\)) = Force \(\times\) Displacement
$$W = F \times s$$ $$W = (mg) \times h$$ $$W = mgh$$

This work done is stored in the object as its Gravitational Potential Energy (\(E_p\)).

Simple machines are basic mechanical devices that make our work easier by multiplying the force applied (mechanical advantage) or by changing the direction of the force. They do not decrease the total work done, but they reduce the effort required.

Examples:

1. Lever: A seesaw or a crowbar.
2. Pulley: Used to draw water from a well.
3. Inclined Plane: A ramp used to load heavy boxes into a truck.

Given:
Force of friction (\(F\)) = 250 N
Displacement (\(s\)) = 50 m

Formula:
$$W = F \times s$$ $$W = 250 \times 50 = 12500 \text{ J}$$

Type of Work Done: Since the force of friction acts in the opposite direction to the displacement, the angle between them is \(180^\circ\). Therefore, the work done by friction is Negative Work (-12500 J).

Answer: (c) - Since \(E_k \propto v^2\), doubling \(v\) makes it \((2v)^2 = 4v^2\). (Difficulty: Medium)

Answer: (c) - An electric motor is a complex machine driven by electricity. (Difficulty: Easy)

Answer: (d) (Difficulty: Easy)

Answer: (c) Zero - Force of gravity is downwards, displacement is horizontal (angle is \(90^\circ\)). (Difficulty: Medium)

Answer: (c) Potential Energy (Elastic potential energy due to change in shape). (Difficulty: Easy)

Answer: 1 Joule is the amount of work done when a force of 1 Newton displaces a body through a distance of 1 meter in the direction of the force.

Answer: Yes. Momentum is zero when the object is at rest (\(v = 0\)). However, if it is at a certain height, it still possesses Potential Energy (which is a form of mechanical energy). (Difficulty: Medium)

Answer:
$$1 \text{ kWh} = 1 \text{ kW} \times 1 \text{ hour}$$ $$1 \text{ kWh} = 1000 \text{ W} \times 3600 \text{ s}$$ $$1 \text{ kWh} = 3,600,000 \text{ J} = 3.6 \times 10^6 \text{ J}$$

Answer: A single fixed pulley does not multiply the force, but it makes work easier by changing the direction of the force applied (we pull downwards to lift a load upwards, using our body weight).

Answer:

• Statement: Energy can neither be created nor destroyed; it can only be transformed from one form to another.
• Illustration: Consider a body of mass \(m\) at a height \(h\).
• At highest point: Velocity is 0, so \(E_k = 0\). Potential energy \(E_p = mgh\). Total Energy = \(mgh\).
• During fall: Height decreases, so \(E_p\) decreases. Velocity increases, so \(E_k\) increases. The loss in \(E_p\) is exactly equal to the gain in \(E_k\).
• Just before hitting the ground: Height is 0, so \(E_p = 0\). Velocity is maximum, \(E_k = \frac{1}{2}mv^2\). Total Energy = \(\frac{1}{2}mv^2\) (which equals the initial \(mgh\)). Thus, total energy remains constant at every point. (Difficulty: Hard)

Answer:

Given: Power (\(P\)) = 1500 W = 1.5 kW. Time (\(t\)) = 10 h.

Energy in Commercial Units (kWh):
$$E = P \times t = 1.5 \text{ kW} \times 10 \text{ h} = 15 \text{ kWh} \text{ (or 15 units)}$$

Energy in Joules:
Since \(1 \text{ kWh} = 3.6 \times 10^6 \text{ J}\),
$$E = 15 \times 3.6 \times 10^6 \text{ J} = 54 \times 10^6 \text{ J} = 5.4 \times 10^7 \text{ J}$$ (Difficulty: Hard)

a) What kind of energy does Rahul have when he is resting at the top of the hill? (Ans: Gravitational Potential Energy)

b) As he rolls down, how is his energy transforming? (Ans: Potential Energy is transforming into Kinetic Energy)

c) Why did he use gears while going up? (Ans: The gear acts as a simple machine, increasing mechanical advantage and reducing the effort needed to push against gravity). (Difficulty: Medium)

Answer: (A) Both are true, and R correctly explains A. When angle is \(90^\circ\), work is zero. (Difficulty: Medium)

Answer: (D) A is false, but R is true. Both do the same work (\(mgh\)), but Boy A has more power because he takes less time (\(P = W/t\)). (Difficulty: Hard)