📘 Work and Energy – Question Paper + Answer Key

✅ Answer

C

🧠 Explanation

Work is done only when a force produces displacement. In physics: \(W = F \times s\).

💡 Did You Know

If you carry a heavy school bag straight on a flat road, your body feels tired, but in physics (ideal case), work done on the bag can be \(0\) because displacement is sideways while force you apply is mostly upward.

✅ Answer

B

🧠 Explanation

Energy and work share the same SI unit: Joule (J).

💡 Did You Know

When a 1 Newton force moves an object by 1 meter, the work done is 1 Joule. That’s why \(1J = 1N \cdot m\).

✅ Answer

C

🧠 Explanation

Kinetic energy: \(E_k=\frac{1}{2}mv^2\). It depends on \(v^2\), so speed matters a lot.

💡 Did You Know

A bicycle at 20 km/h has 4 times more kinetic energy than the same bicycle at 10 km/h (because speed doubles → \(v^2\) becomes 4 times).

✅ Answer

C

🧠 Explanation

Kinetic energy is energy due to motion. A moving car is in motion.

💡 Did You Know

Even a slowly moving cricket ball has kinetic energy. That’s why it can break a window at high speed.

✅ Answer

C

🧠 Explanation

Gravitational potential energy: \(PE = mgh\).

💡 Did You Know

If you lift a 1 kg book by 1 meter, you increase its potential energy by about \(9.8J\) (taking \(g \approx 9.8 m/s^2\)).

✅ Answer

B

🧠 Explanation

Power is rate of doing work: \(P=\frac{W}{t}\). Unit is Watt (W).

💡 Did You Know

A 60W bulb uses 60 Joules of energy every second. That’s why wattage matters in electricity bills.

✅ Answer

C

🧠 Explanation

\(1kW = 1000W\). “kilo” means 1000.

💡 Did You Know

If a 1kW heater runs for 1 hour, it consumes 1 unit (1 kWh) of electricity.

✅ Answer

C

🧠 Explanation

Energy changes form but total remains constant in an isolated system.

💡 Did You Know

In car brakes, kinetic energy doesn’t vanish. It converts mainly into heat due to friction.

✅ Answer

B

🧠 Explanation

Mechanical energy = Kinetic energy + Potential energy.

💡 Did You Know

A swinging pendulum keeps converting energy: top point has more PE, middle has more KE.

✅ Answer

C

🧠 Explanation

Power tells how fast work is done: \(P=\frac{W}{t}\).

💡 Did You Know

Two students climb the same stairs. Whoever reaches faster has higher power output (same work, less time).

✅ Answer

Kinetic

🧠 Explanation

Energy due to motion is kinetic energy.

💡 Did You Know

Even a moving fan blade has kinetic energy. Faster rotation means more kinetic energy.

✅ Answer

Joule

🧠 Explanation

Work and energy share the same unit: Joule (J).

💡 Did You Know

A 10N force moving 1m does 10J of work.

✅ Answer

1/2 mv²

🧠 Explanation

In LaTeX: \(E_k=\frac{1}{2}mv^2\).

💡 Did You Know

That’s why overspeeding is dangerous: small speed increase causes big KE increase.

✅ Answer

Potential

🧠 Explanation

Energy due to position/height is potential energy.

💡 Did You Know

Water stored in a dam has huge potential energy that can generate electricity.

✅ Answer

Work

🧠 Explanation

In LaTeX: \(P=\frac{W}{t}\).

💡 Did You Know

Same work in half the time means double the power.

✅ Answer

Energy is the capacity to do work.

🧠 Explanation

If you can do work (push, lift, move), you have energy in some form.

💡 Did You Know

Food gives chemical energy. Your body converts it into mechanical energy when you run.

✅ Answer

Watt

🧠 Explanation

Power = work per time. \(1W = 1J/s\).

💡 Did You Know

A mixer grinder can be 500W–750W, meaning it uses energy very fast.

✅ Answer

Kinetic energy

🧠 Explanation

It’s moving, so it has kinetic energy.

💡 Did You Know

A flying bird at height has both KE (motion) and PE (height). In exams, answer is usually KE.

✅ Answer

P=W/t

🧠 Explanation

In LaTeX: \(P=\frac{W}{t}\).

💡 Did You Know

Same work, less time = more power. Like finishing the same homework faster.

✅ Answer

Electric bulb (electrical → light)

🧠 Explanation

Electrical energy converts mainly to light and some heat.

💡 Did You Know

An electric iron converts electrical energy to heat energy. That’s why it becomes hot.

✅ Answer

Work is done when force causes displacement.

🧠 Explanation

Physics formula: \(W = F \times s\) (when force and displacement are along same line).

💡 Did You Know

If you hold a bucket of water without moving it, your hands get tired, but work done on the bucket is \(0\) because \(s=0\).

✅ Answer

Energy due to motion is kinetic energy. Formula: 1/2 mv^2

🧠 Explanation

In LaTeX: \(E_k=\frac{1}{2}mv^2\).

💡 Did You Know

A fast cricket ball has much more KE than a slow one, so it can hurt more. Speed matters more than mass because of \(v^2\).

✅ Answer

Stored energy due to position or shape is potential energy. Example: lifted stone.

🧠 Explanation

Gravitational PE: \(PE=mgh\). Elastic PE comes due to stretching/compressing.

💡 Did You Know

A bow (archery) stores elastic potential energy when stretched. On release, it converts into kinetic energy of the arrow.

✅ Answer

Power is rate of doing work. SI unit: watt.

🧠 Explanation

Formula: \(P=\frac{W}{t}\). SI unit: Watt (W).

💡 Did You Know

A lift (elevator) needs more power than a staircase climb because it does the same work for many people in less time.

✅ Answer

Mechanical energy is sum of kinetic and potential energy.

🧠 Explanation

Mechanical energy \(=\) KE \(+\) PE.

💡 Did You Know

In a roller coaster, mechanical energy shifts between KE and PE. Friction converts some into heat, so total mechanical energy reduces (but total energy overall is conserved).

✅ Answer (As it is)

📘 Law of Conservation of Energy The Law of Conservation of Energy states that: Energy can neither be created nor destroyed. It can only be converted from one form to another. The total energy of a system remains constant. This law is valid at all times and for all kinds of energy transformations. ________________________________________ 🧪 Example: Freely Falling Object Consider an object of mass m falling freely from a height h. 🔹 At the top: Velocity = 0 Kinetic Energy (KE) = 0 Potential Energy (PE) = \(mgh\) 👉 Total Energy = \(mgh\) ________________________________________ 🔹 During the fall: Height decreases ⬇️ Speed increases 🚀 PE decreases KE increases At any point: \[ \text{Total Energy} = \text{PE} + \text{KE} \] ________________________________________ 🔹 Just before touching the ground: Height ≈ 0 Velocity is maximum PE ≈ 0 KE is maximum \[ KE = \frac{1}{2}mv^2 \] 👉 Total energy remains same. ________________________________________ 📐 Mathematical Expression \[ mgh + \frac{1}{2}mv^2 = \text{constant} \] ________________________________________ 🧠 Conclusion Potential energy changes into kinetic energy Total mechanical energy remains constant Energy is not lost, only transformed (Air resistance is ignored) ________________________________________ 🌟 Main Point 🔹 Energy is conserved 🔹 PE converts to KE 🔹 Total energy remains unchanged

🧠 Explanation

Key idea: total energy stays constant. For a falling body: \(PE = mgh\), \(KE = \frac{1}{2}mv^2\), so \[ mgh + \frac{1}{2}mv^2 = \text{constant} \]

💡 Did You Know (Example)

A swinging playground swing is a perfect real-life example: Top position → more PE, less KE. Middle position → less PE, more KE. It keeps converting energy back and forth, just like your falling object example.

✅ Answer (As it is)

📘 Given Let: Mass of object = m Initial velocity = u Final velocity = v Acceleration = a Displacement = s ________________________________________ 🧮 Step 1: Work Done Work done is given by: \[ W = \text{Force} \times \text{Displacement} \] Using Newton’s second law: \[ F = ma \] So, \[ W = ma \times s \] ________________________________________ 🧮 Step 2: Use Equation of Motion \[ v^2 - u^2 = 2as \] \[ s = \frac{v^2 - u^2}{2a} \] ________________________________________ 🧮 Step 3: Substitute value of s \[ W = ma \times \frac{v^2 - u^2}{2a} \] \[ W = \frac{1}{2} m (v^2 - u^2) \] ________________________________________ 🧮 Step 4: Special Case (Object starts from rest) If \(u = 0\): \[ W = \frac{1}{2} mv^2 \] ________________________________________ 📐 Final Expression \[ \boxed{E_k = \frac{1}{2} mv^2} \] ________________________________________ 🧠 Conclusion Kinetic energy depends on mass and square of velocity More speed → much more kinetic energy ________________________________________ 🌟 Main Point 🔹 Kinetic energy is energy of motion 🔹 Formula: \(E_k = \frac{1}{2} mv^2\) 🔹 Speed has a greater effect than mass

🧠 Explanation

Using \(W=Fs\), \(F=ma\), and \(v^2-u^2=2as\), we get: \(W=\frac{1}{2}m(v^2-u^2)\). If \(u=0\), \(E_k=\frac{1}{2}mv^2\).

💡 Did You Know (Example)

Why trucks need longer braking distance? Because KE depends on \(v^2\). If a truck doubles its speed, its kinetic energy becomes 4 times, so brakes must remove 4 times energy (more distance + more heat).