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Physics (SSC Physics)NCTB SSC Physics (Classes 9-10)All 13 ChaptersKinematics & DynamicsOptics & Electricity

SSC Physics Equation & Solution Suite

All-in-one NCTB SSC Physics textbook calculator covering all 13 chapters: Kinematics, Forces, Work-Power-Energy, Hydrostatic Pressure, Heat, Sound, Optics, and Electricity.

CalculatorFormulasExemplarsCasio fx-991ApplicationsFAQ
SSC Physics Unified Solution SuiteNCTB 9-10

13-Chapter Interactive Physics Solver

Gravity (g):
Kelvin Scale:
2. Motion & KinematicsID: #ch2
কাঙ্ক্ষিত রাশি নির্ণয়:
Velocity-Time Graph & Displacement Areas = ut + ½at²
t (s)v (m/s)0u=10v=20.0t=5sArea s = 75.0 m
Step-by-Step Derivation
Calculated Value:
20m/s
1. Given Data
u=10 m/s,a=2 m/s2,t=5 su = 10\text{ m/s}, \quad a = 2\text{ m/s}^2, \quad t = 5\text{ s}
2. First Equation of Motion
v=u+atv = u + at
3. Evaluation
v=10+(2×5)=20 m/sv = 10 + (2 \times 5) = 20\text{ m/s}
কাসিও সাইন্টিফিক ক্যালকুলেটর শর্টকাটের জন্য নিচে দেখুনfx-991EX / MS
Result:
20m/s

Formula & Derivation

Theoretical foundation, dimensional analysis, and governing boundary conditions.

NCTB SSC Physics 13-Chapter Comprehensive Formula Sheet

SSC board exams test physical principles through both Creative Questions (CQ - 50 marks) and Multiple Choice Questions (MCQ - 25 marks). Master all fundamental formulas below:

Ch 1: Physical Quantities & Measurement

• Vernier Constant: VC = s / N

• Slide Calipers: L = M + (V × VC) - E

• Screw Gauge LC: LC = p / N

• Sphere Volume: V = 4/3 π r³

Ch 2: Motion (Kinematics)

• v = u + at

• s = ((u + v)/2) × t

• s = ut + 1/2 at²

• v² = u² + 2as

• Vertical projection: H_max = u² / (2g), T = 2u / g

Ch 3: Force & Dynamics

• Force: F = ma

• Momentum: p = mv

• Momentum conservation: m1u1 + m2u2 = m1v1 + m2v2

• Inelastic collision: v = (m1u1 + m2u2) / (m1 + m2)

• Gravitational force: F = G (m1·m2) / d²

Ch 4: Work, Power & Energy

• Mechanical work: W = F·s·cos(θ)

• Kinetic energy: Ek = 1/2 mv²

• Potential energy: Ep = mgh

• Power: P = W / t (1 HP = 746 W)

• Efficiency: η = (P_useful / P_total) × 100%

Ch 5: Pressure & States of Matter

• Pressure: P = F / A

• Hydrostatic pressure: P = h·ρ·g

• Hydraulic press: F1 / r1² = F2 / r2²

• Young's Modulus: Y = (F·L) / (A·ΔL)

Ch 6: Effect of Heat on Matter

• Temperature conversion: C/5 = (F-32)/9 = (K-273)/5

• Thermal expansion: ΔL = α L1 Δθ, β = 2α, γ = 3α

• Heat transfer: Q = m·s·Δθ

• Latent heat: Q = m·Lf (ice: 336000), Q = m·Lv

Ch 7: Waves & Sound

• Wave velocity: v = f·λ, f = 1 / T

• Sound speed with temperature: v_θ = 332 + 0.6·θ

• Echo relation: 2d = v·t

• Min echo distance: d_min = (v × 0.1) / 2

Ch 8 & 9: Geometric Optics (Mirrors & Lenses)

• Mirror equation: 1/f = 1/u + 1/v

• Magnification: m = -v/u, |m| = hi / ho

• Snell's Law: η1·sin(θ1) = η2·sin(θ2)

• Critical angle: sin(θc) = η_rare / η_dense

• Optical lens power: P = 1 / f (in meters) Dioptres

Ch 10 & 11: Static & Current Electricity

• Coulomb's Law: F = k (q1·q2) / r²

• Field intensity & potential: E = kQ/r², V = kQ/r

• Ohm's Law & resistivity: V = IR, R = ρ L / A

• Resistors: Rs = Σ R, 1/Rp = Σ (1/R)

• Commercial electricity: kWh = (P·t) / 1000

Ch 12 & 13: Magnetism & Modern Physics

• Ideal transformer: Vp / Vs = Np / Ns = Is / Ip

• Einstein mass-energy: E = m c²

• Radioactive decay: N(t) = N0 · (1/2)^(t / T_half)

• Decay constant: λ = 0.693 / T_half

Solved Textbook Examples

Three fully worked pedagogical exemplars: standard textbook, advanced edge-case, and authentic past board examination.

Board Exam Special (Kinematics & Vertical Projection)bg-amber-500/10 text-amber-400 border border-amber-500/20
A cricket ball is projected vertically upward with an initial velocity of 19.6 m/s. Find the maximum height reached and the total time of flight before it hits the ground. (Take g = 9.8 m/s²)
Given Parameters:
  • Initial velocity u = 19.6 m/s
  • Acceleration due to gravity g = 9.8 m/s²
  • Velocity at highest point v = 0 m/s
Procedural Solution:
Equation for maximum height: v² = u² - 2gH_max ⟹ 0 = u² - 2gH_max ⟹ H_max = u² / (2g)
H_max = (19.6)² / (2 × 9.8) = 384.16 / 19.6 = 19.6 meters.
Time to reach peak: t_rise = u / g = 19.6 / 9.8 = 2 seconds.
Total time of flight: T = 2 × t_rise = 2 × 2 = 4 seconds.
Final Answer:The ball reaches a maximum height of 19.6 meters and returns to the ground in 4 seconds.
Board Exam Special (Work, Power & Efficiency)bg-emerald-500/10 text-emerald-400 border border-emerald-500/20
An electric water pump has a rated power of 2 Horsepower (2 HP). It lifts 500 kg of water from a 10-meter deep well in 1 minute. Calculate the mechanical efficiency (η) of the pump. (Take g = 9.8 m/s²)
Given Parameters:
  • Total power input P_total = 2 HP = 2 × 746 W = 1492 Watts
  • Mass of water m = 500 kg, Height h = 10 m, Time t = 60 s
  • Acceleration due to gravity g = 9.8 m/s²
Procedural Solution:
Work done against gravity: W = mgh = 500 × 9.8 × 10 = 49,000 Joules.
Useful power output: P_useful = W / t = 49,000 / 60 = 816.67 Watts.
Efficiency formula: η = (P_useful / P_total) × 100%
η = (816.67 / 1492) × 100% = 54.74%
Final Answer:The mechanical efficiency of the water pump is 54.74%.
Board Exam Special (Waves, Sound Speed & Echo)bg-cyan-500/10 text-cyan-400 border border-cyan-500/20
On a day when the air temperature is 30°C, a student claps their hands in front of a tall mountain. What is the minimum distance required to hear a distinct echo? (Take sound speed at 0°C v0 = 332 m/s)
Given Parameters:
  • Air temperature θ = 30°C
  • Speed of sound at 0°C v0 = 332 m/s
  • Persistence of hearing t = 0.1 seconds
Procedural Solution:
Speed of sound at 30°C: v_θ = v0 + 0.6 × θ = 332 + (0.6 × 30) = 332 + 18 = 350 m/s.
Round trip echo distance: 2d = v × t ⟹ d = (v × t) / 2.
For minimum distance, taking t = 0.1 s: d_min = (350 × 0.1) / 2 = 35 / 2 = 17.5 meters.
Final Answer:The minimum distance to the obstacle mountain is 17.5 meters at 30°C.
Board Exam Special (Current Electricity & Billing)bg-purple-500/10 text-purple-400 border border-purple-500/20
A household runs five 60W incandescent light bulbs and two 100W ceiling fans for 6 hours daily. If each electrical unit costs 7.50 BDT, compute the total electricity bill for May (31 days).
Given Parameters:
  • 5 bulbs power = 5 × 60 W = 300 W
  • 2 fans power = 2 × 100 W = 200 W, Total power P = 500 Watts
  • Daily usage t = 6 hours, Month of May = 31 days, Tariff rate = 7.50 BDT/unit
Procedural Solution:
Total energy consumed in Board of Trade (BOT) units (kWh): W = (P × t_daily × days) / 1000
W = (500 × 6 × 31) / 1000 = 93,000 / 1000 = 93 kWh.
Total electricity bill = Units × Tariff Rate = 93 × 7.50 = 697.50 BDT.
Final Answer:The total monthly electricity bill for May is 697.50 BDT.

Casio Scientific Calculator Keystroke GuideExam Ready

Exact button sequences permitted in board and university entrance examination halls:

Casio fx-991ES PLUS / 2nd Edition
Newton-Raphson numerical solver directly on COMP mode.
1. Write Equation with Red Equals Sign
ALPHACALC(=)
Combine ALPHA + CALC for "=" and ALPHA + ) for variable X.
2. Press SHIFT + CALC
SHIFTCALC
Shows "Solve for X".
3. Press = to Calculate
=
Wait 1 second for iteration convergence.

Practical Applications

How this scientific principle drives chemical engineering, aerospace, medicine, and research.

Board Exam Tips & Pitfalls:

  • Unit Conversion: Always convert km/h to m/s by dividing by 3.6 (e.g. 54 km/h = 15 m/s). Convert grams to kg by dividing by 1000.
  • Mirror & Lens Focal Sign: Remember that convex mirrors and concave lenses have negative focal lengths (-f). Omitting the negative sign in exam steps leads to zero marks.
  • Electricity Billing: Power must be in Watts and time in total hours before dividing by 1000 to obtain BOT units (kWh).
  • Offline Practice: You can run our zero-dependency Python CLI agent (scripts/ssc_physics_calculator.py) on your laptop without an internet connection.

Frequently Asked Questions

Answers to common conceptual misconceptions and board examination guidelines.

What default value of gravity (g) does NCTB specify for secondary exams?▼
NCTB secondary curriculum textbooks in Bangladesh standardize on g = 9.8 m/s². Our calculator defaults to 9.8 m/s² with an instant toggle to 9.81 m/s² for higher precision or international exam benchmarks (such as Edexcel or Cambridge O-Levels).
Why is 0.1 seconds the critical threshold for hearing an echo?▼
The human auditory sensation persists in the brain for approximately 0.1 seconds after the sound wave ceases. If a reflected sound wave returns in under 0.1 seconds, it overlaps with the original sensation. Only when round-trip travel time t >= 0.1 s is a distinct echo perceived.
What are the sign conventions for spherical mirrors and thin lenses?▼
For spherical mirrors: Concave mirrors have positive focal lengths (+f) while convex mirrors have negative focal lengths (-f). For thin lenses: Convex lenses have positive focal lengths (+f) and concave lenses have negative focal lengths (-f). Real images correspond to positive v, while virtual images produce negative v.
How do I solve multi-step kinematics equations on a Casio scientific calculator?▼
On Casio fx-991EX / ClassWiz and fx-991CW, store physical parameters into variable memories (A, B, C) via the STO key, and compute formulas in one go using the natural textbook display.