Physics Grade 12 · Unit 15 Model Paper · Athens Academy Islamabad

FBISE · Exam March 2027 · Total Marks: 68

Time allowed
2 hours 35 minutes

Section B
42 marks

Section C
26 marks

Coverage
Unit 15 only

Section A — Multiple Choice

Not printed in this paper. Section A is delivered on the Athens Academy portal.

Before you attempt this paper, complete the Unit 15 Quiz and revise the Unit 15 Flashcards on the portal. Those cover the full MCQ range for this unit — Newton's law of gravitation, gravitational field strength, orbital velocity, geostationary satellites, and gravitational potential and potential energy.

Section A carries 17 marks (17 MCQs × 1). Those marks are shown in the Board Marking Pattern table at the end of this paper and are recorded on the portal, not here.

Section B — Short Response Questions

Note: Attempt any FOURTEEN parts. Each part carries 3 marks. Where an OR alternative is given, attempt only one of the two. (14 × 3 = 42)

(3)★When a satellite is put into a higher orbit, what will be the effect on its orbital velocity? Explain mathematically. (1 + 2)

ORState Newton's law of universal gravitation and write its mathematical form, naming each symbol and its unit.
(3)★Find the gravitational field strength $g$ at a height of $1500~\text{km}$ above the surface of the Earth. $(R_E = 6.4 \times 10^{6}~\text{m},\ g = 9.8~\text{m s}^{-2})$

ORDefine gravitational field strength. Write its formula and SI unit, and state why it is numerically equal to the acceleration due to gravity.
(3)What factors determine the strength of the gravitational field $g$ around a planet? (1.5 + 1.5)

ORTwo planets have the same mass but different radii. How would their gravitational field strengths compare? Justify with the formula.
(3)Show that Newton's law of gravitation is consistent with Newton's third law of motion.

ORWhy does an apple fall towards the Earth due to gravity, while the Earth does not visibly move towards the apple?
(3)★Derive the equation $g = \dfrac{G M_E}{R_E^{2}}$ for the gravitational field strength at the surface of the Earth, and state why it is independent of the mass of the falling body.

ORWhat will be the value of $g$ on an exoplanet whose mass is five times that of Earth and whose radius is twice that of Earth? $(g_{Earth} = 9.8~\text{m s}^{-2})$
(3)★Derive the expression $v_o = \sqrt{\dfrac{G M_E}{r}}$ for the orbital velocity of a satellite, stating why it is independent of the satellite's own mass.

ORWhy do satellites in higher orbits have lower orbital velocities? Explain with the mathematical relation.
(3)What is a geostationary satellite? State any two conditions its orbit must satisfy.

ORHow does the mass of the Earth affect the orbital velocity required for a satellite to stay in orbit? Justify with the formula.
(3)★A satellite orbits the Earth at an altitude equal to the Earth's radius. Calculate its orbital speed. $(M_E = 6 \times 10^{24}~\text{kg},\ R_E = 6.4 \times 10^{6}~\text{m})$

ORCalculate the gravitational force between two bodies of masses $45~\text{kg}$ and $50~\text{kg}$ placed $1~\text{m}$ apart. $(G = 6.67 \times 10^{-11}~\text{N m}^{2}\,\text{kg}^{-2})$
(3)Define gravitational potential. Write its formula and SI unit, and explain why its value is negative.

ORIs it possible for an object's gravitational potential energy to become negative? If so, what does this mean for the object's motion? (1.5 + 1.5)
(3)★Explain why the equation $\Delta \text{P.E.} = mgh$ cannot be used far from the Earth's surface, and state which expression replaces it.

ORHow is the gravitational potential energy of two point masses related to the concept of gravitational potential?
(3)Explain, using gravitational field lines, how the direction and strength of a gravitational field are represented for a point mass.

ORWhy is $g$ approximately constant for small changes in height near the Earth's surface? Justify using the altitude formula.
(3)★Determine the free-fall acceleration at the surface of Jupiter. $(m_J = 1.898 \times 10^{27}~\text{kg},\ r_J = 7.15 \times 10^{7}~\text{m},\ G = 6.67 \times 10^{-11}~\text{N m}^{2}\,\text{kg}^{-2})$

ORWhy can gravitation not account for the formation of molecules, and why don't two books on a desk attract each other noticeably?
(3)Explain the uniform-sphere approximation: for a point outside a uniform sphere, where may its mass be considered to act, and why is this useful?

ORGravitational force between two objects is $F$ . If both masses are doubled and the distance between their centres is halved, find the new force in terms of $F$ .
(3)★The Hubble Space Telescope is in a circular orbit $613~\text{km}$ above the Earth's surface. Calculate its orbital speed. $(M_E = 6 \times 10^{24}~\text{kg},\ R_E = 6.4 \times 10^{6}~\text{m})$

ORCan gravitational field strength be negative? Explain your answer with reference to its definition.
(3)Define absolute gravitational potential energy. State the reference point used and explain the sign of the result.

ORWhy do we say that the law of gravitation is a universal law? Give two reasons.
(3)★To launch a satellite around Mars at an altitude of $300~\text{km}$ , calculate its orbital velocity. $(m_{Mars} = 6.42 \times 10^{23}~\text{kg},\ r_{Mars} = 3.39 \times 10^{6}~\text{m})$

ORIf a satellite's launch speed is too low or too high, describe what happens to its path in each case.

Section C — Long Questions

Note: Attempt any TWO questions. Marks are shown at the end of each part. (2 × 13 = 26)

(2 + 4 + 1)(a)★Briefly describe gravitational potential and derive the expression $V = -\dfrac{G M_E}{r}$ at a distance $r$ from the centre of the Earth. Make a sketch.

(6)(b)What is the gravitational potential energy and gravitational potential with respect to the Sun at the position of the Earth? $(M_S = 1.99 \times 10^{30}~\text{kg},\ M_E = 6 \times 10^{24}~\text{kg},\ r = 1.5 \times 10^{11}~\text{m})$
(2 + 5)(a)★What are gravitational field and gravitational field strength? Derive the formula for gravitational acceleration $g$ at the surface of the Earth, and discuss the variation of $g$ with altitude.

(6)(b)Determine the free-fall acceleration at the surface of Jupiter, and hence the weight of a $60~\text{kg}$ astronaut standing on it. $(m_J = 1.898 \times 10^{27}~\text{kg},\ r_J = 7.15 \times 10^{7}~\text{m})$
(2 + 5)(a)★What are geostationary satellites? Derive the expression for the orbital radius $r = \left(\dfrac{G M_E T^{2}}{4\pi^{2}}\right)^{1/3}$ , and hence describe how the orbital speed and the height above the surface are obtained.

(6)(b)Calculate the orbital radius of a geostationary satellite of the Earth. $(G = 6.67 \times 10^{-11}~\text{N m}^{2}\,\text{kg}^{-2},\ M_E = 6 \times 10^{24}~\text{kg},\ T = 86400~\text{s})$
(1 + 4 + 2)(a)★State Newton's law of universal gravitation. Explain how it is consistent with Newton's third law of motion, and describe how the gravitational force varies with the distance between two masses.

(6)(b)Two stars of a binary system, Alpha Centauri A $(2.19 \times 10^{30}~\text{kg})$ and Alpha Centauri B $(1.80 \times 10^{30}~\text{kg})$ , attract each other with a force of $2.24 \times 10^{25}~\text{N}$ . Find the distance between the two stars.

Board Marking Pattern

FBISE HSSC-II Physics — pattern followed in this paper (single-unit adaptation)
Section	Type	Structure	Marks
A	Multiple choice	17 MCQs × 1 — on the Athens portal, not printed here	17
B	Short response	Attempt any 14 parts × 3 marks (each with an OR alternative)	42
C	Long response	Attempt any 2 of 4 questions × 13 marks	26
Total (Sections B & C)			68

How to use this paper

Give yourself 2 hours 35 minutes and sit the whole paper in one attempt, without notes.
In Section B, read both options before choosing. The OR alternative is often the shorter answer.
Every numerical must show the six steps: Given → Required → Formula → Substitution → Calculation → ∴ Answer. Marks are given for the steps, not only the final number.
Measure every distance $r$ from the centre of the body, and for satellites use $r = R_E + h$ — not the height alone.
Keep the minus sign on gravitational potential and potential energy. Dropping it loses the concept mark.
Carry the SI unit through to the final line of every answer. A correct number without a unit loses a mark.

— END OF PAPER —

Athens Academy Islamabad · Physics · Grade 12 · Unit 15 — Gravitation · FBISE · Exam March 2027

Unit Model Paper — Unit 15: Gravitation

Section A — Multiple Choice

Section B — Short Response Questions

Section C — Long Questions

Board Marking Pattern

📃 Chapter 15 · Gravitation — Chapter Model Paper

FBISE Grade 12 Physics — Chapter 15: Gravitation Model Paper