CG Board Class 9 Science Chapter 12 Solutions: Work and Energy (कार्य एवं ऊर्जा) – 2026-27

In which of the following situations is work being done according to science? State reasons for your answer:

1. You pushed a very large stone, but it did not move.
2. You reached the second floor of a building by climbing stairs.
3. A traveller pulls his luggage to some distance on a platform.
4. Stopping a moving bicycle.

No work done. Force was applied, but the displacement of the stone was zero (S = 0).

Work is done. The person applies force against gravity to displace their body vertically upwards to the second floor.

Work is done. The traveller applies a pulling force on the luggage, causing displacement along the platform in the direction of applied force.

Work is done (Negative work). The braking force is applied opposite to the direction of motion to displace the bicycle to a stop.

A box filled with books is placed near a wall. Even after several efforts by you, the box does not move. Calculate the work done according to the equation W = FS.

• Applied Force = F
• Displacement (S) = 0 m
• W = F × S = F × 0 = 0 Joules.
• Reason: Since there is no displacement, no physical work is done on the box.

Can you think of a situation where there is displacement in the absence of any force? Discuss.

Yes. According to Newton’s First Law of Motion, an object moving with a uniform velocity in deep outer space (where gravitational and frictional forces are completely absent) continues to displace indefinitely at constant velocity without requiring any external force (F = 0).

A ball is thrown upwards. A gravitational force continuously acts on it in the downward direction.

1. Which force acting on the ball does positive work?
2. Which force on the ball does negative work?
3. Support your answer with reasons.

The throwing force applied by the hand during the launch performs positive work because force and initial upward displacement are in the same direction.

The gravitational force performs negative work while the ball moves upwards.

When displacement is opposite to the direction of applied force, the work done is negative (W = -fS). Here, gravity acts downwards while displacement is upwards.

A student picks up an object of mass m in the vertical direction to a height h and moves a distance d horizontally. How much work is done by the student in raising the object and walking horizontally?

• Work done in lifting vertically: W₁ = mgh (since applied lifting force F = mg is in the direction of vertical displacement h).
• Work done while walking horizontally: W₂ = 0 (since the uniform horizontal velocity implies zero horizontal acceleration and zero horizontal force, F = 0).
• Total Work Done: W = W₁ + W₂ = mgh + 0 = mgh.

What do you mean by kinetic energy of an object?

The energy possessed by an object due to its state of motion is called kinetic energy. Formula: E_k = 1/2mv².

The kinetic energy of a body of mass m moving at a velocity v is 1/2mv². If its velocity is doubled, how much will be its kinetic energy?

• Initial Kinetic Energy = E_k1 = 1/2mv².
• New velocity = v’ = 2v.
• New Kinetic Energy = E_k2 = 1/2m(2v)² = 1/2m(4v²) = 4 (1/2mv²) = 4 E_k1.
• The kinetic energy becomes 4 times its initial value.

If the velocity and mass of an object are twice the velocity and mass of another object, how much will be the ratio of their kinetic energies?

• Let object 1 have mass m₁ = m and velocity v₁ = v.
• E_k1 = 1/2mv².
• For object 2: m₂ = 2m and v₂ = 2v.
• E_k2 = 1/2(2m)(2v)² = 1/2(2m)(4v²) = 8 (1/2mv²) = 8 E_k1.
• Ratio (E_k1)/(E_k2) = 1/8 or E_k2 : E_k1 = 8 : 1.

A cuboidal box is shown in Fig. 16. Its width and height are 2h and h respectively. What will be the potential energy of an object of mass m placed on the box when placed vertically vs horizontally?

Height above ground = h. Gravitational Potential Energy = E_p = mgh.

Height above ground = 2h. Gravitational Potential Energy = E_p = m × g × (2h) = 2mgh.

In the process of using a bow and arrow, why do we have to pull the arrow backwards by using a thread or rubber?

When the string/rubber is stretched backwards, muscle work done against elasticity gets stored as elastic potential energy in the stretched string. On releasing, this potential energy converts into kinetic energy of the arrow, propelling it forward at high speed.

Can the gravitational potential energy of an object be negative?

Yes. Potential energy depends on the chosen reference zero-level. If a position below the chosen reference surface (e.g., inside a deep well or pit) is considered, the height h is negative, making E_p = -mgh negative.

A person of mass m jumps into a swimming pool from a height of 10 m. Using the law of conservation of mechanical energy, calculate the velocity of the man when he is at a height of 5 m from the water surface.

1. What do you mean by power?
2. Define 1 watt power.
3. If a bulb consumes 990 Joules of electric energy in 10 sec, how much will be its power?

The rate of doing work or rate of energy conversion is called power. Formula: P = W/t.

If an agent performs 1 Joule of work in 1 second, its power is 1 Watt (1 W = 1 J/s).

(i) If an object displaces 2 m in the direction of 10 N applied force, the work done on the object by the force is:**

(ii) A body of mass 5 kg is in a constant motion at 2 m/s. What will be its kinetic energy?

(iii) A body of 12 kg mass is placed at a certain height from the surface of earth. If its potential energy is 480 J, then what will be its height w.r.t. earth’s surface?

(iv) You burn a bulb of 100 W daily for 5 hours. What will be the energy spent in units by the bulb in one day?

(i) SI unit of work is …………………………**

(ii) 1 kwh is equivalent to ……………………….. joules.

(iii) The total energy of an object remains ………………………….

(iv) If the direction of applied force of an object and its displacement are opposite then its work will be ………………………………

• Step 1: Relation between Units and Joules / यूनिट तथा जूल में संबंध:
• 1 unit = 1 kWh = 3.6 × 10⁶ J (or 36 × 10⁵ J).
• Step 2: Conversion / रूपांतरण:
• Energy consumed = 250 units = 250 × 3.6 × 10⁶ J.
• Energy in Joules = 900 × 10⁶ J = 9 × 10⁸ Joules.

Energy can neither be created nor destroyed; it can only be converted from one form to another. The total energy of an isolated system remains constant.

No, it does not contradict the law. As the body falls, its height decreases, causing potential energy (E_p = mgh) to decrease. However, its speed increases due to gravitational acceleration, causing an equal increase in kinetic energy (E_k = 1/2mv²). The sum of potential and kinetic energy (E_p + E_k) remains constant at all points.

The energy stored in an object due to its position or change in shape is called its potential energy.

Kinetic energy is proportional to the square of velocity (E_k ∝ v²). Doubling velocity (2v) increases kinetic energy to (2)² = 4 times.

According to the Work-Energy Theorem (Δ E_k = W), if W = 0, the change in kinetic energy is zero, meaning velocity remains constant (unchanged).

The stopping distance will be 4d (four times the initial distance).

No physical work is done (W = 0).**

• Reason: Although the man exerts an upward force to balance the weight of the sack, there is zero displacement (S = 0) of the sack while standing stationary.

• Given Values / दिए गए मान:
• Force (F) = 8 N
• Displacement (S) = 4 m
• Formula & Calculation / सूत्र एवं गणना:
• W = F × S = 8 N × 4 m = 32 Joules (J).

• Given Values / दिए गए मान:
• Mass (m) = 10 kg
• Height (h) = 10 m
• Acceleration due to gravity (g) = 9.8 m/s² (or 10 m/s²)
• W = mgh = 10 kg × 9.8 m/s² × 10 m = 980 Joules (J).
• (If using g = 10 m/s²: W = 10 × 10 × 10 = 1000 J).

• Step 1: Potential Energy of First Body (E_p1) / प्रथम पिंड की स्थितिज ऊर्जा:
• m₁ = 10 kg, h₁ = 5 m, g = 9.8 m/s²
• E_p1 = m₁ g h₁ = 10 × 9.8 × 5 = 490 Joules
• Step 2: Potential Energy of Second Body (E_p2) / द्वितीय पिंड की स्थितिज ऊर्जा:
• m₂ = 15 kg, h₂ = 2 m, g = 9.8 m/s²
• E_p2 = m₂ g h₂ = 15 × 9.8 × 2 = 294 Joules
• Step 3: Difference in Potential Energies / स्थितिज ऊर्जाओं का अंतर:
• Δ E_p = E_p1 – E_p2 = 490 – 294 = 196 Joules (J).
• (If using g = 10 m/s²: E_p1 = 500 J, E_p2 = 300 J, Difference = 200 J).

• Step 1: Total Mechanical Energy at Position A (h_A = 10 m) / स्थिति A पर कुल ऊर्जा:
• Initial speed u = 0 ⇒ E_kA = 0
• E_pA = m g h_A = m × 9.8 × 10 = 98m Joules
• Total Energy = 98m
• Step 2: Total Mechanical Energy at Position D (h_D = 2.5 m) / स्थिति D पर कुल ऊर्जा:
• E_pD = m g h_D = m × 9.8 × 2.5 = 24.5m Joules
• E_kD = 1/2mv_D²
• Step 3: Apply Conservation Law / ऊर्जा संरक्षण नियम लागू करने पर:
• E_pA + E_kA = E_pD + E_kD
• 98m + 0 = 24.5m + 1/2mv_D²
• 98m – 24.5m = 1/2mv_D² ⇒ 73.5m = 1/2mv_D²
• Cancel m: v_D² = 73.5 × 2 = 147
• v_D = √(147) ≈ 12.12 m/s.
• (If using g = 10 m/s²: 100m – 25m = 1/2mv_D² ⇒ 75 = 1/2v_D² ⇒ v_D = √(150) ≈ 12.25 m/s).

• Step 1: Calculate Work Done (W) / किए गए कार्य की गणना:
• Force (F) = 15 N, Displacement (S) = 8 m
• W = F × S = 15 × 8 = 120 Joules (J)
• Step 2: Calculate Power (P) / शक्ति की गणना:
• Time (t) = 6 s
• P = W/t = 120/6 = 20 Watts (W).

• Given Values / दिए गए मान:
• Mass (m) = 0.5 kg
• Potential Energy (Δ E_p) = 1 Joule
• Acceleration due to gravity (g) = 10 m/s²
• Formula & Step-by-Step Calculation / सूत्र एवं गणना:
• E_p = mgh
• 1 = 0.5 × 10 × h
• 1 = 5h ⇒ h = 1/5 = 0.2 meters (or 20 cm).