JEE Main Pattern Practice Questions

Close the Book. Start the Clock.

Sections 1 to 11 and 13 taught you this chapter — Kepler's three laws, the universal law and superposition, both shell theorems, $g$ and the three ways it varies, potential energy and potential, escape speed, orbital speed and period, the energy of a bound orbit, geostationary and polar satellites, weightlessness, forty-odd worked problems and two exam-specific toolkits. This section asks one different question: can you use any of it with a timer running?

There is no new theory below. There are 30 single-correct questions built to the exam pattern, and a marking scheme designed to punish the two habits this chapter rewards most cruelly — reaching for a formula before checking which radius it wants, and writing a potential where a potential energy belongs.

The rules of engagement

Key Point: This is not a reading exercise. Blank sheet, pen, timer. Attempt all 30 questions in one unbroken sitting, and do not open a single explanation until the last answer is written.

The constants sheet

Every question that needs a number uses these and no others. Copy them to the top of your sheet before you start.

Those numbers are internally consistent: $\sqrt{2gR_E} = \sqrt{2(9.8)(6.4\times10^6)} = 11\,200$ m/s exactly, and $\frac{11.2}{\sqrt{2}} = 7.9$ km/s. Never mix 9.8 and 10 inside one problem — the 2% difference is enough to move you between two adjacent options.

[Exam Tip] That $-1$ is not decoration. Four wild guesses that land one lucky hit earn $4 - 3 = +1$ mark for four minutes of work — a terrible trade. But a question narrowed to two options returns $\frac{4 - 1}{2} = +1.5$ marks on average, which is a very good one. Narrow first, then commit. Leave blank only what you could not narrow at all.

What this set covers

That spread mirrors how the paper actually samples this chapter. Potential and the variation of $g$ are 10 of the 30, because between them they carry the most marks here — and they are the two places where a confident wrong answer is easiest to produce. A potential quoted where a potential energy was wanted; $\frac{2h}{R_E}$ used at a height where the binomial has long stopped being honest; $R_E$ written where $R_E + h$ belonged.

The difficulty mix is roughly 20% easy, 45% medium and 35% hard. A handful will feel brutal. They are meant to.

[Exam Tip] Before you start, write four lines at the top of your sheet: which radius — $R_E$, $R_E + h$, or $R_E - d$?, is this $U$ or $V$?, what is the sign?, and is anything conserved here? Those four questions decide the method for almost every problem below, and choosing the method is where the marks in this chapter are actually won.

Scoring Yourself Honestly

Mark your sheet with the real scheme — $+4$, $-1$, $0$ — and total it. No half marks for "I knew that one really". The number you get is the number that matters.

The bands

Read your own answer sheet

Before you touch a single explanation, sort your mistakes into three piles. This is the most valuable ten minutes in the whole section.

1. Method errors — you used $mgh$ where the height was comparable with $R_E$, or conserved energy across a manoeuvre in which a rocket did work. You treated the field inside a shell as zero and concluded the potential was zero too. You applied the depth formula $g_d = g\left(1 - \frac{d}{R_E}\right)$ to a height. These are the expensive ones, because the whole solution is wrong from line one.
2. Execution errors — right method, wrong arithmetic. The classic three in this chapter: forgetting to add $R_E$ to a height quoted above the surface, losing the factor 2 between $\frac{GMm}{r}$ and $\frac{GMm}{2r}$, and dropping a minus sign so that a bound orbit comes out with positive total energy.
3. Reading errors — the question asked for the potential, not the potential energy; for the speed at aphelion, not perihelion; for the binding energy, not the total energy; for a depth, not a height.

Key Point: In this chapter pile 3 is dominated by four traps: $U$ or $V$, which radius, what sign, and above or below the surface. Check which of the four caught you, every single time.

The eight habits this set is drilling

• Name the radius before you name the formula. $R_E$ is the surface, $R_E + h$ is a point above it, $R_E - d$ is a point below it, and $r$ in an orbital formula is measured from the centre of the Earth, never from the ground.
• $U$ and $V$ are different quantities. $V$ is measured in J/kg and belongs to the point; $U = mV$ is measured in joules and belongs to the body you put there. A question that gives you a mass wants $U$; a question that does not wants $V$.
• A zero field does not mean a zero potential. Inside a shell the field vanishes everywhere and the potential is a perfectly definite $-\frac{GM}{R}$. At the null point between two masses the field cancels and the potential does not.
• Every $U$ and every $V$ in this chapter is negative, with the zero taken at infinity. A bound orbit has $E < 0$. Binding energy is $-E$, and it is positive. If a sign comes out the other way, you have made an error, not a discovery.
• $mgh$ is a near-surface approximation. It is the first term of $\frac{GM_Em h}{R_E(R_E+h)}$, and it is honest only while $h \ll R_E$. The moment a question says "at a height equal to the Earth's radius", $mgh$ is finished.
• In a circular orbit, $K = -E$ and $U = 2E$. Learn the triple once and half the energy questions in this chapter become one line.
• Kepler's third law needs the semi-major axis, not the perigee distance. For a circle they coincide; for an ellipse they do not, and the question that hands you a perigee and an apogee is testing exactly that.
• Check the size of the answer. A satellite cannot orbit faster than 7.9 km/s. Nothing launched from the surface at less than 11.2 km/s gets away. The period of any Earth satellite is at least 84.6 minutes.

[Exam Tip] Every explanation below is a full step-by-step solution, so this set doubles as revision. Read the explanation even for the questions you got right — several of these have a two-line route and a two-page route, and it is the two-line route you will need in the hall.