JEE Main Physics — Practice Set 1

Kinematics, laws of motion, work and energy, rotational motion, thermodynamics, current electricity and modern physics — at JEE Main difficulty, with the shortcut alongside the full derivation.

How to use this: JEE Main gives roughly 2 minutes per question with negative marking on MCQs. Speed comes from recognising the standard result, not from deriving it under pressure. Where a shortcut exists below, learn the shortcut.

Kinematics and Laws of Motion

1. A body is projected at $60°$ to the horizontal with speed $20\ \text{m/s}$. Find its maximum height. (g = 10 m/s²)

        u² sin²θ
H  =  ------------
          2g

        (20)² × (sin 60°)²        400 × (√3/2)²
   =  ---------------------  =  ----------------
              2(10)                    20

        400 × 0.75
   =  --------------  =  15 m
             20

Answer: 15 m

Standard results to have memorised, not derived:

$$H = \frac{u^2\sin^2\theta}{2g} \qquad R = \frac{u^2\sin 2\theta}{g} \qquad T = \frac{2u\sin\theta}{g}$$

Deriving these in the exam costs you a question elsewhere.

2. A block of mass 2 kg rests on a rough surface with $\mu = 0.4$. What minimum horizontal force starts it moving? (g = 10 m/s²)

f_max = μN = μmg = 0.4 × 2 × 10 = 8 N

Any force exceeding 8 N initiates motion.

Answer: 8 N

The trap: using the kinetic coefficient when the question asks what starts motion. Starting requires overcoming static friction, which is the larger of the two.

3. Two blocks of 3 kg and 2 kg are connected by a string over a frictionless pulley. Find the acceleration. (g = 10 m/s²)

Treat the system as one mass; the net driving force is the weight difference:

       (m₁ - m₂)g      (3 - 2)(10)      10
a  =  ------------- = ------------- = ------ = 2 m/s²
        m₁ + m₂          3 + 2           5

Answer: 2 m/s²

Tension, if asked: $T = \dfrac{2m_1m_2g}{m_1+m_2} = \dfrac{2(3)(2)(10)}{5} = 24\ \text{N}$

Sense check: $T$ must lie between the two weights (20 N and 30 N). 24 N does. If your tension falls outside that range, you have a sign error.

Work, Energy and Rotation

4. A force $\vec{F} = 3\hat{i} + 4\hat{j}$ N moves a body through $\vec{d} = 2\hat{i} - \hat{j}$ m. Find the work done.

W = F⃗ · d⃗
  = (3)(2) + (4)(-1)
  = 6 - 4
  = 2 J

Answer: 2 J

Remember: work is a scalar (dot) product. Producing a vector answer means you used the cross product, which gives torque, not work.

5. A solid sphere and a hollow sphere of equal mass and radius roll down an incline from rest. Which reaches the bottom first?

Answer: the solid sphere.

For rolling without slipping:

              g sin θ
a  =  -------------------
         1 + I/(mR²)

Solid sphere:  I = (2/5)mR²  ⟹  a = g sin θ / 1.4 = 0.714 g sin θ
Hollow sphere: I = (2/3)mR²  ⟹  a = g sin θ / 1.667 = 0.6 g sin θ

The principle, which generalises: the smaller the value of $I/mR^2$, the greater the acceleration. Mass and radius cancel entirely — only the mass distribution matters. Ranking by that ratio answers every question of this type instantly:

6. A wheel of moment of inertia $2\ \text{kg m}^2$ accelerates from rest to $10\ \text{rad/s}$ in 5 s. Find the torque.

        ω - ω₀      10 - 0
α  =  ---------- = -------- = 2 rad/s²
           t          5

τ = Iα = 2 × 2 = 4 N m

Answer: 4 N m

Note the parallel: $\tau = I\alpha$ is the rotational $F = ma$. Every linear relation has a rotational twin — $m \to I$, $v \to \omega$, $F \to \tau$, $p \to L$. Learning the map halves what you memorise.

Thermodynamics

7. An ideal gas undergoes an isothermal expansion. Which statement is true?

(a) $\Delta U > 0$ (b) $\Delta U = 0$ (c) $Q = 0$ (d) $W = 0$

Answer: (b)

For an ideal gas, internal energy depends only on temperature. Isothermal means $\Delta T = 0$, so $\Delta U = 0$, and the first law gives $Q = W$.

Distinguish carefully:

Option (c) is the adiabatic condition, placed there for candidates who confuse the two.

8. A Carnot engine operates between 500 K and 300 K. Find its efficiency.

          T_cold          300
η = 1 - --------- = 1 - ------- = 1 - 0.6 = 0.4  =  40%
          T_hot           500

Answer: 40%

Temperatures must be in kelvin. Using Celsius is the single most common error in this question type.

Current Electricity

9. Three resistors of 6 Ω each are connected in parallel. Find the equivalent resistance.

For n identical resistors in parallel:  R_eq = R/n = 6/3 = 2 Ω

Answer: 2 Ω

Shortcut worth internalising: $n$ identical resistors in parallel give $R/n$; in series they give $nR$. This appears constantly and needs no working.

10. A wire of resistance $R$ is stretched to twice its length. Find the new resistance.

Stretching conserves volume:  A₁L₁ = A₂L₂
If L₂ = 2L₁, then A₂ = A₁/2

        ρL₂        ρ(2L₁)          ρL₁
R₂ =  ------- =  ------------ = 4 ------  = 4R
         A₂         A₁/2            A₁

Answer: $4R$

General result: stretching to $n$ times the length multiplies resistance by $n^2$. Candidates who forget that the area also changes answer $2R$ — the most-chosen wrong option.

Modern Physics

11. The work function of a metal is 2.0 eV. Find the maximum kinetic energy of photoelectrons for incident light of energy 5.0 eV.

K_max = E - φ = 5.0 - 2.0 = 3.0 eV

Answer: 3.0 eV

Einstein's photoelectric equation: $K_{max} = h\nu - \phi$. Note that $K_{max}$ depends on frequency, never on intensity; intensity governs the number of photoelectrons. JEE tests that distinction directly and often.

12. Find the de Broglie wavelength of an electron accelerated through 100 V.

              12.27
λ (in Å)  =  --------  ,  V in volts
              √V

              12.27       12.27
          =  -------- =  -------  =  1.227 Å  =  1.227 × 10⁻¹⁰ m
              √100         10

Answer: ≈ 1.23 Å

Memorise the numeric form $\lambda = 12.27/\sqrt{V}$ Å for electrons. Deriving it from $\lambda = h/\sqrt{2mqV}$ works but costs a minute you do not have.

How to convert preparation into JEE Main marks

1. Standard results, not derivations. Projectile formulas, $I/mR^2$ ratios, $12.27/\sqrt{V}$ — recall beats derivation under a two-minute budget.
2. Sense-check with limits. Tension between the two weights; parallel resistance below the smallest; efficiency below 1. These catch sign and algebra errors in seconds.
3. Track units, especially kelvin. Thermodynamics questions are frequently lost on Celsius alone.
4. Negative marking rewards discipline. −1 for a wrong MCQ answer. Eliminate at least one option before guessing; skip cleanly when you cannot.
5. Numerical-value questions have no negative marking in the current pattern — attempt all of them.

Where to go next

• CBSE Class 12 Physics Practice Paper 1 — the same physics at board depth
• NEET Biology Practice Set 1 — if you are keeping the medical route open
• SAT Math Practice Set 1 — for overseas applications

Ask StudyAI for more JEE-level questions on any topic here, with the standard results drilled separately from the derivations.