HP TGT Non-Medical exam mein Physics ke numericals sabse zyada Work, Energy aur Power se aate hain. Yeh chapter dikhne mein aasaan lagta hai, par isme "Negative Work" aur "Conservation of Energy" ke concepts aksar students ko confuse karte hain.
Aaj hum is chapter ko exam point of view se deep mein samjhenge. Kya aap jante hain ki chalti hui gaadi mein break lagane par "Work Done" negative kyun hota hai? Aaiye jaante hain.
1. Work (Karya) - The Physics Definition
Aam bhasha mein padhna ya sochna kaam hai, lekin Physics mein Work tabhi hota hai jab Force lagne par Displacement (Visthapan) ho.
Formula:
$$W = F s \cos\theta$$(Jahan $\theta$ Force aur Displacement ke beech ka angle hai).
Types of Work (Exam Special):
| Type | Angle (θ) | Example |
| Positive Work | $0^\circ$ (Same Dir) | Girti hui ball (Gravity dwara work). |
| Negative Work | $180^\circ$ (Opposite) | Zameen par ghisatti cheez par Friction dwara kiya gaya kaam. |
| Zero Work | $90^\circ$ (Perpendicular) | Coolie ka sar par bojh lekar chalna (Force upar, Motion aage). |
2. Energy (Urja)
Energy is the capacity to do work. Iski unit bhi Joule (J) hai.
A. Kinetic Energy (Gatij Urja):
Motion ki wajah se jo energy hoti hai.
Formula:
$$K.E. = \frac{1}{2}mv^2$$Relation with Momentum (Most Important for TGT):
Agar Momentum ($p$) diya ho, toh KE kaise nikalenge?
$$K.E. = \frac{p^2}{2m}$$Trick: Agar Momentum Double (2x) karein, toh KE 4 guna (4x) ho jayegi.
B. Potential Energy (Sthitij Urja):
Position ya shape ki wajah se energy.
Gravitational PE:
$$P.E. = mgh$$(Height par stored energy).
Spring PE:
$$P.E. = \frac{1}{2}kx^2$$(Khichi hui spring mein).
3. Work-Energy Theorem (Karya-Urja Pramey)
Yeh theorem numericals solve karne ka "Brahmastra" hai.
Statement: Kisi body par kiya gaya Work done uski Kinetic Energy mein change ke barabar hota hai.
$$W = \Delta K.E. = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$$Example: Agar gaadi rokni hai, toh Brake dwara kiya gaya kaam gaadi ki KE khatam karne mein kharch hoga.
4. Conservation of Energy
Energy na paida hoti hai na khatam, bas roop (form) badalti hai.
Falling Object: Jab ball upar se girti hai:
Top: Max PE, Zero KE.
Middle: PE + KE mix.
Bottom: Zero PE, Max KE.
Total Energy: Hamesha Constant ($PE + KE = Constant$).
5. Power (Shakti)
Rate of doing work.
Formula:
$$P = \frac{W}{t} = F \times v$$(Force $\times$ Velocity bhi Power hota hai).
Unit: Watt (W).
Horse Power (HP): Machines ki taakat HP mein napte hain.
$$1 \text{ H.P.} = 746 \text{ Watt}$$
Commercial Unit of Energy:
Ghar ki bijli Units mein aati hai.
1 Unit = 1 kWh (Kilowatt-hour).
Value:
$$1 \text{ kWh} = 3.6 \times 10^6 \text{ Joules}$$
6. Important Formulas Table
| Concept | Formula |
| Work | $W = Fs \cos\theta$ |
| KE & Momentum | $K = \frac{p^2}{2m}$ |
| Spring Energy | $U = \frac{1}{2}kx^2$ |
| Power | $P = F \times v$ |
| Work-Energy Theorem | $W = K_f - K_i$ |
7. HP TGT Special MCQs (Exam Level)
Q1. If the momentum of a body is increased by 100%, its kinetic energy will increase by:
A) 100%
B) 200%
C) 300%
D) 400%
Ans: C
(Hint: $p' = 2p$, so $K' \propto (2p)^2 = 4K$. Change = $4K - K = 3K = 300\%$).
Q2. A coolie lifts a bag of 10kg to a height of 2m. Work done against gravity is: ($g=10$)
A) 20 J
B) 200 J
C) 0 J
D) 100 J
Ans: B (Formula: $mgh = 10 \times 10 \times 2 = 200J$).
(Note: Lifting mein work hota hai, lekar khade rehne mein zero hota hai).
Q3. 1 Kilowatt-hour (kWh) is equal to:
A) $3.6 \times 10^5$ J
B) $3.6 \times 10^6$ J
C) $746$ J
D) $1000$ J
Ans: B
Q4. A light and a heavy body have equal kinetic energy. Which one has greater momentum?
A) Light body
B) Heavy body
C) Both equal
D) Cannot say
Ans: B (Formula: $p = \sqrt{2mK}$. Since $K$ is same, $p \propto \sqrt{m}$. Heavy mass means more momentum).
Q5. The area under Force-Displacement graph represents:
A) Power
B) Work Done
C) Impulse
D) Acceleration
Ans: B
8. Collisions (Sanghatt/Takkar) - Advanced Concept
Jab do bodies takrati hain, toh momentum hamesha conserve rehta hai, lekin Energy ka kya? Yeh concept TGT ke liye bohot zaroori hai.
Types of Collision:
Elastic Collision (Poornatah Pratyasth):
Momentum: Conserved.
Kinetic Energy: Conserved (Loss nahi hoti).
Forces: Conservative hote hain.
Example: Ideal gas molecules ki takkar, ya steel balls ki takkar.
Inelastic Collision (Apratyasth):
Momentum: Conserved.
Kinetic Energy: Loss hoti hai (Heat/Sound mein badal jati hai).
Example: Do gaadiyon ka accident, ya gili mitti (mud) ka diwar par chipakna.
Coefficient of Restitution ($e$):
Takkar ke baad body kitni speed se alag hoti hai, use '$e$' kehte hain.
Elastic Collision: $e = 1$
Inelastic Collision: $0 < e < 1$
Perfectly Inelastic: $e = 0$ (Bodies chipak jati hain).
9. Potential Energy of a Spring (Spring ki Urja)
Agar aap kisi spring ko khinchte ya dabate hain, toh usme energy store ho jati hai.
Hooke’s Law: Spring force displacement ke vipreet lagta hai.
$$F = -kx$$(Jahan $k$ = Spring Constant, $x$ = Displacement).
Stored Energy Formula:
$$U = \frac{1}{2}kx^2$$Exam Trick: Agar spring ko aadha (half) kaat diya jaye, toh uska Spring Constant ($k$) dugna (double) ho jata hai. (Chhote spring ko khinchna mushkil hota hai).
10. Motion in a Vertical Circle (Urdhvadhar Vrit)
Maut ka Kuan (Death Well) ya rassi se bandha patthar ghumana iska example hai. Gravity ki wajah se speed har jagah badalti hai.
Lowest Point (Bottom): Rassi tootne ka darr sabse zyada yahin hota hai.
Minimum Velocity to complete circle:
$$v = \sqrt{5gr}$$
Highest Point (Top):
Minimum Velocity to not fall down:
$$v = \sqrt{gr}$$
Horizontal Point (Middle):
Velocity:
$$v = \sqrt{3gr}$$
11. Efficiency of a Machine (Dakshta)
Machine kitni acchi hai, yeh uski efficiency se pata chalta hai. Ideal machine ki efficiency 100% hoti hai, par real life mein friction ki wajah se kam hoti hai.
Formula:
$$\text{Efficiency } (\eta) = \frac{\text{Output Power}}{\text{Input Power}} \times 100$$
12. Transformation of Energy (Urja Rupantaran)
Exams mein matching questions aate hain: "Dynamo kya karta hai?"
| Device (Yantra) | Transformation (Badlav) |
| Dynamo / Generator | Mechanical Energy $\rightarrow$ Electrical Energy |
| Electric Motor | Electrical Energy $\rightarrow$ Mechanical Energy |
| Microphone | Sound Energy $\rightarrow$ Electrical Energy |
| Loudspeaker | Electrical Energy $\rightarrow$ Sound Energy |
| Battery / Cell | Chemical Energy $\rightarrow$ Electrical Energy |
| Solar Cell | Light Energy $\rightarrow$ Electrical Energy |
13. Advanced Numericals (Mains Level)
Problem 1 (Spring):
A spring of force constant $k = 100 N/m$ is stretched by $10 cm$. Calculate energy stored.
Solution:
$x = 10 \text{ cm} = 0.1 \text{ m}$.
$U = \frac{1}{2}kx^2 = \frac{1}{2} \times 100 \times (0.1)^2$
$U = 50 \times 0.01 = \mathbf{0.5 \text{ Joules}}$.
Problem 2 (Power):
An engine pumps 100 kg water to a height of 10m in 10 seconds. Calculate Power. ($g=10$)
Solution:
Work ($W$) = $mgh = 100 \times 10 \times 10 = 10,000 \text{ J}$.
Power ($P$) = $W/t = 10,000 / 10 = \mathbf{1000 \text{ Watts}}$ (or $1 \text{ kW}$).
Conclusion
Work, Energy aur Power physics ke wo pillars hain jo Mechanics ko samajhne mein madad karte hain. TGT exam ke liye $p^2/2m$ wala relation aur Work-Energy Theorem sabse important hain.
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