Numericals with Answers - Work and Energy | Science Class 9 PDF Download

The study of Class 9 Science  Chapter - Work and Energy  explores how forces cause motion and how energy transforms in the world around us. You’ll learn about the scientific meaning of work, the different forms of energy like kinetic and potential energy, the law of conservation of energy, and the concept of power. 

These ideas will help you understand everyday phenomena—like lifting objects, moving vehicles, or even a swinging Pendulum—and how energy is transferred and conserved. 

Basic Formulae

Work Done: Work is done when a force causes displacement in its direction.

• If force and displacement are in the same direction: W = F × S
• If force is at an angle θ to the displacement: W = F × S × cos(θ)
• Unit: Joule (J), where 1 J = 1 Nm.
• Work is zero if displacement is zero or if the force is Perpendicular to the displacement (cos 90° = 0).
• Work is positive if force and displacement are in the same direction, negative if opposite.

Kinetic Energy (K.E.): The energy of an object due to its motion.

K.E. = ½mv²

m = mass (kg), v = velocity (m/s), K.E. in Joules (J).

Potential Energy (P.E.): The energy of an object due to its position (height).

P.E. = mgh

m = mass (kg), g = acceleration due to gravity (use 10 m/s² unless specified), h = height (m), P.E. in Joules (J).

Law of Conservation of Energy: Energy cannot be created or destroyed; it transforms from one form to another.

Total mechanical energy (K.E. + P.E.) remains constant in a system with no external forces.

K.E. + P.E. = constant.

Power: The rate of doing work or transferring energy.

P = W / t

W = work done (J), t = time (s), P in Watts (W), 1 W = 1 J/s.

Larger units: 1 kW = 1000 W, 1 MW = 10⁶ W, 1 hp = 746 W.

Solved Examples

Q1: An object of mass 10 kg is moving at a velocity of 20 m/s. If the object comes to rest after covering 40 m, calculate the average retarding force.

Sol: Initial Kinetic Energy = ½ × 10 × 20² = 100 × 20 = 2000 J
Work done by retarding force = -Force × Displacement
⇒ -F × 40 = -2000
⇒ F = 2000 / 40 = 50 N

Q2: A boy pulls a cart with a force of 30 N at an angle of 60° to the horizontal. If the cart moves 8 m horizontally, calculate the work done by the boy. (Use cos 60° = 0.5)

Sol: Formula: W = F × S × cos(θ)

Given: F = 30 N, S = 8 m, θ = 60°, cos 60° = 0.5

W = 30 × 8 × cos 60° = 30 × 8 × 0.5 = 120 J

Q3: A crane does 18000 J of work in 15 seconds. Calculate its power in kilowatts (kW).

Sol: Formula: P = W / t

Given: W = 18000 J, t = 15 s

P = 18000 / 15 = 1200 W

Convert to kW: 1 kW = 1000 W

P = 1200 / 1000 = 1.2 kW

Q4: A stone of mass 2 kg is dropped from a height of 8 m. Calculate the velocity of the stone just before it hits the ground, assuming no air resistance. (Take g = 10 m/s²)

Sol: By the law of conservation of energy, P.E. at the top = K.E. just before hitting the ground.

Initial Potential Energy, E = m g h

Given: m = 2 kg, g = 10 m/s², h = 8 m

P.E. = 2 × 10 × 8 = 160 J

By conservation of energy, all the potential energy converts to kinetic energy.

⇒ Kinetic Energy (K.E.) at the ground = 160 J 

Formula: K.E. = ½mv²

160 = ½ × 2 × v²

160 = v²

v = √160 = √(16 × 10)
 = 4√10 ≈ 4 × 3.16 = 12.64 m/s (using √10 ≈ 3.16)

Q5: A Pendulum bob of mass 0.5 kg is released from a height of 4 m above its lowest point. Calculate its potential energy at the top, kinetic energy at the lowest point, and kinetic energy when it is 1 m above the lowest point. (Take g = 10 m/s²)

Sol: Step 1: Potential energy at the top.

Formula: P.E. = mgh

Given: m = 0.5 kg, g = 10 m/s², h = 4 m

P.E. = 0.5 × 10 × 4 = 20 J

Step 2: Kinetic energy at the lowest point (h = 0).

By conservation of energy, total mechanical energy is conserved.

At the top: P.E. = 20 J, K.E. = 0 (since velocity = 0).

Total energy = 20 J

At the lowest point: P.E. = 0 (h = 0), so K.E. = 20 J

Step 3: Kinetic energy at h = 1 m above the lowest point.

P.E. at h = 1 m = mgh = 0.5 × 10 × 1 = 5 J

Total energy = 20 J (constant)

K.E. = Total energy - P.E. = 20 - 5 = 15 J

 P.E. at the top = 20 J, K.E. at the lowest point = 20 J, K.E. at 1 m above the lowest point = 15 J

Q6: A lift raises 1500 kg of material to a height of 12 m in 1 minute. Calculate the power of the lift in watts. (Take g = 10 m/s²)

Sol: Step 1: Calculate work done (work = potential energy gained).

Formula: W = mgh

Given: m = 1500 kg, g = 10 m/s², h = 12 m

W = 1500 × 10 × 12 = 180000 J

Step 2: Convert time to seconds.

t = 1 minute = 60 s

Step 3: Calculate power.

Formula: P = W / t

P = 180000 / 60 = 3000 W

Q7: An object at a height of 4 m above the ground has a potential energy of 800 J. Calculate the mass of the object. (Take g = 10 m/s²)

Sol: Formula: P.E. = m g h

Given: P.E. = 800 J, g = 10 m/s², h = 4 m

800 = m × 10 × 4

800 = 40m

m = 800 / 40 = 20 kg

Q8: Two objects, A and B, have masses 3 kg and 6 kg, respectively, and are moving with velocities 5 m/s and 3 m/s. Compare their kinetic energies.

Sol: Formula: K.E. = ½mv²

For object A: m = 3 kg, v = 5 m/s

K.E._A = ½ × 3 × (5)² = ½ × 3 × 25 = 37.5 J

For object B: m = 6 kg, v = 3 m/s

K.E._B = ½ × 6 × (3)² = ½ × 6 × 9 = 27 J

Ratio: K.E._A : K.E._B = 37.5 : 27 = 37.5 / 27 = 1.39 (approx.)

K.E. of A : K.E. of B ≈ 1.39 : 1

Q9: A sled is pushed with a force of 70 N at an angle of 30° to the horizontal for 20 m forward, then pushed back 10 m with the same force and angle. Calculate the total work done by the force. (Use cos 30° = 0.866, cos 150° = -0.866)

Sol: Forward motion:

Formula: W = F × S × cos(θ)

Given: F = 70 N, S = 20 m, θ = 30°, cos 30° = 0.866

W₁ = 70 × 20 × 0.866 = 1212.4 J

Backward motion: Force at 150° to displacement (opposite direction).

S = 10 m, θ = 150°, cos 150° = -0.866

W₂ = 70 × 10 × cos 150° = 70 × 10 × (-0.866) = -606.2 J

Total work done = W₁ + W₂ = 1212.4 + (-606.2) = 606.2 J

Q10: An object of mass 10 kg has a potential energy of 2940 J at a certain height. If the acceleration due to gravity is 9.8 m/s², calculate the height.

Sol: Formula: P.E. = m g h

Given: P.E. = 2940 J, m = 10 kg, g = 9.8 m/s²

2940 = 10 × 9.8 × h

2940 = 98h

h = 2940 / 98 = 30 m