JEE Mains Physics Formula Sheet: Key Results and Shortcuts

This JEE mains physics formula sheet gathers results that turn long problems into short ones, such as the rolling acceleration $a = \frac{g \sin\theta}{1 + (k/R)^2}$ . JEE Main physics draws on what you study in Classes 11 and 12, but its questions combine ideas, so the sheet stresses derived results, limiting cases and shortcuts on top of the textbook formulas.

Treat it as a physics formula sheet for JEE revision written for this site; it is not issued by the exam's conducting body, and JEE Main does not normally supply a formula sheet, so check the current information bulletin for the rules. The basics of each chapter are on the Class 11 list and the Class 12 sheet, and other courses are on the formula sheets hub.

Quick facts

Syllabus base
Class 11 and Class 12 physics
Style
Multi concept problems, numerical answers as well as options
Rolling result
$a = \frac{g\sin\theta}{1 + k^2/R^2}$
Error rule
For Z = AᵖBᵠ, ΔZ/Z = pΔA/A + qΔB/B
Must know
Calculus, vectors, graphs and dimensions
Handy values
hc ≈ 1240 eV nm, 1 u ≈ 931.5 MeV/c²

Measurement, errors and dimensions

Units and measurement results
Result	When JEE uses it	Unit	Explained
$\frac{\Delta Z}{Z} = p\frac{\Delta A}{A} + q\frac{\Delta B}{B}$	maximum fractional error of a power law	no unit	Dimensional formulas explained
$[M^a L^b T^c]$	checking or building a formula by dimensions	no unit	Force dimensions explained
$\text{LC} = 1\ \text{MSD} - 1\ \text{VSD}$	least count of a vernier caliper	m	Units explained

Example 1: error in g from a pendulum

A student finds g from $g = \frac{4\pi^2 L}{T^2}$ . The length has a 1.0% error and the period a 0.5% error. What is the maximum percentage error in g?

$\frac{\Delta g}{g} = \frac{\Delta L}{L} + 2\frac{\Delta T}{T} = 1.0\% + 2(0.5\%) = 2.0\%$ .

Answer: 2.0%. The power of T doubles its share, which is why timing many oscillations improves the result.

Mechanics results worth memorising

Advanced mechanics
Result	When JEE uses it	Unit	Explained
$a = \frac{\Delta m}{M}\,g$	Atwood machine, light pulley: Δm the mass difference, M the total	m/s²	Tension explained
$F = v_{rel}\frac{dm}{dt}$	thrust when mass is ejected (rockets, conveyor)	N	Thrust explained
$v = \sqrt{\mu_s rg}$	top speed on a flat circular road	m/s	Banking explained
$a = \frac{g\sin\theta}{1 + I/(mR^2)}$	rolling without slipping down an incline	m/s²	Radius of gyration explained
$E = -\frac{GMm}{2r}$	total energy of a satellite in a circular orbit	J	Orbital velocity explained
$T = 2\pi\sqrt{\frac{r^3}{GM}}$	orbital period	s	Satellite period explained
$v_{cm} = \frac{m_1v_1 + m_2v_2}{m_1 + m_2}$	center of mass velocity, unchanged with no external force	m/s	Center of mass explained

Example 2: which rolls fastest

A solid sphere rolls without slipping down a slope inclined at 37° (take sin 37° = 0.6). Find its acceleration, and compare with a ring.

For a solid sphere $k^2/R^2 = 2/5$ , so $a = \frac{(9.8)(0.6)}{1.4} = 4.2\ \text{m/s}^2$ .

For a ring $k^2/R^2 = 1$ , so $a = \frac{(9.8)(0.6)}{2} = 2.94\ \text{m/s}^2$ . Answer: 4.2 m/s² for the sphere; the ring, with more of its mass far from the axis, is slower.

Heat, thermodynamics and waves

Thermal physics and oscillations
Result	When JEE uses it	Unit	Explained
$W = nRT\ln\frac{V_2}{V_1}$	isothermal work done by an ideal gas	J	First law explained
$PV^\gamma = \text{constant}$	adiabatic change of an ideal gas	Pa m³ᵞ	Thermodynamics explained
$\frac{dT}{dt} = -k(T - T_0)$	cooling of a hot body	K/s	Newton's law of cooling explained
$f' = f\,\frac{v \pm v_o}{v \mp v_s}$	Doppler effect for sound	Hz	Speed of sound explained
$v = \sqrt{\frac{\gamma P}{\rho}}$	Laplace's result for sound through a gas	m/s	Sound speed explained
$I \propto A^2 f^2$	intensity of a wave	W/m²	Intensity explained

In the Doppler formula, use the upper signs when source and observer move towards each other.

Electricity and magnetism on the jee mains physics formula sheet

Electrostatics, circuits, magnetism and AC
Result	When JEE uses it	Unit	Explained
$C = \frac{\varepsilon_0 A}{d - t + t/K}$	capacitor partly filled with a slab of thickness t	F	Capacitance explained
$q = q_0\left(1 - e^{-t/RC}\right)$	charging through a resistor	C	RC charging explained
$f = \frac{qB}{2\pi m}$	cyclotron frequency	Hz	Lorentz force explained
$\vec{\mu} = NI\vec{A}$	magnetic moment of a coil	A m²	Magnetic moment explained
$\cos\phi = \frac{R}{Z}$	power factor of an LCR circuit	no unit	Impedance explained
$M = \mu_0 n_1 n_2 \pi r_1^2 l$	mutual inductance of coaxial solenoids, inner radius r₁	H	Mutual inductance explained

When a capacitor is connected to a battery and a slab is inserted, V stays fixed; when the battery is removed first, Q stays fixed. Decide which before you calculate energy changes.

Optics and modern physics

Light, atoms and nuclei
Result	When JEE uses it	Unit	Explained
$n = \frac{\sin\frac{A + \delta_m}{2}}{\sin\frac{A}{2}}$	refractive index from minimum deviation in a prism	no unit	Angle of deviation explained
$P = P_1 + P_2$	two thin lenses touching, with P = 1/F in dioptres	m⁻¹	Lens power explained
$r_n = (0.053\ \text{nm})\,\frac{n^2}{Z}$	Bohr orbit radius	m	Orbital angular momentum explained
$\frac{1}{\lambda} = RZ^2\left[\frac{1}{n_f^2} - \frac{1}{n_i^2}\right]$	wavelength of a line, electron falling from nᵢ to n_f	m⁻¹	Spectral lines explained
$\lambda = \frac{h}{\sqrt{2mK}}$	de Broglie wavelength from kinetic energy	m	Dual nature explained

Silvered lens questions combine lens and mirror power; see silvering of a lens for the method.

How to revise physics for JEE with a formula sheet

Derive, then memorise. If you can derive the rolling result in two lines, you will not misremember it.
Learn limiting cases. Set m₂ = 0 in the Atwood result and you should get g.
Check units of options. It often eliminates two choices at once.
Keep a mistakes notebook. Note each formula you misapplied and why.

If you are also preparing for the medical entrance, the NEET physics formula sheet focuses on the NCERT core.

Frequently asked questions

Is a formula sheet given in JEE Main?

Students are generally expected to know the formulas, and no sheet is usually supplied. Check the current information bulletin for the rules of your attempt.

Which physics topics carry the most weight in JEE Main?

Mechanics, electricity and magnetism, and modern physics together make up much of the paper, but questions come from every chapter, so do not skip any.

Is this physics formula sheet for JEE Mains enough for JEE Advanced?

It covers the core results, but JEE Advanced asks deeper multi step problems. Use it as a base and add derivations and special cases.

How do I remember so many physics formulas for JEE?

Link them: rotation mirrors linear motion, electric and gravitational fields share inverse square forms, and many results are limiting cases of a general one. Practise daily with mixed problems.