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#	Question	Answer
1	What is the perihelion?	The point in the orbit of a planet nearest to the Sun.
2	Is the time taken by a planet to traverse the arc near the aphelion equal to the time taken to traverse the arc near the perihelion?	No. The planet takes a longer time to traverse the arc near the aphelion.
3	What is the gravitational force on a point mass outside a hollow spherical shell of uniform density?	The same as if the entire mass of the shell were concentrated at its centre.
4	Three equal masses are placed at the vertices of an equilateral triangle. What is the force on a mass \( 2m \) placed at the centroid?	Zero.
5	What is the gravitational potential energy of a particle of mass \( m \) at a distance \( r \) from the centre of the Earth?	\( U = -\frac{G M_E m}{r} \) (taking \( U = 0 \) at infinity).
6	Why is it said that Cavendish 'weighed the Earth'?	Because the measurement of \( G \) combined with the knowledge of \( g \) and \( R_E \) allows the estimation of the mass of the Earth.
7	What is the time period of a satellite in a circular orbit close to the surface of the Earth?	Approximately 85 minutes.
8	What is the orbital speed of a satellite very close to the surface of the Earth?	\( v = \sqrt{gR_E} \).
9	Which quantities are conserved in the motion of an object under the gravitational influence of another object?	Angular momentum and total mechanical energy. Linear momentum is not conserved.
10	Does the acceleration due to gravity increase or decrease with increasing altitude?	Decreases.
11	Does the escape speed depend on the direction of projection?	No.
12	Who proposed the heliocentric model in which planets revolve around a fixed Sun?	Nicolas Copernicus (though the heliocentric idea was first mentioned earlier by Aryabhatta in the 5th century A.D.).
13	Does the choice of the arbitrary constant in gravitational potential energy affect the gravitational force?	No. The gravitational force is not altered by the choice of this constant.
14	Two uniform solid spheres of equal radius R, masses M and 4M, have centres 6R apart. Where is the neutral point (where gravitational forces from both cancel) measured from the centre of the M sphere?	At \( r = 2R \) from the centre of the M sphere.
15	Using the Moon's orbital data (R = 3.84×10⁸ m, T = 27.3 days) and Kepler's third law, what is the mass of the Earth?	\( M_E = 4\pi^2 R^3/(GT^2) \approx 6.02 \times 10^{24} \) kg — within 1% of the value obtained from g and \(R_E\).
16	Io, a moon of Jupiter, has an orbital period of 1.769 days and orbital radius 4.22×10⁸ m. What does this show about Jupiter's mass?	\( M_{Jupiter} \approx 1.9 \times 10^{27} \) kg, about one-thousandth the mass of the Sun (\(2\times10^{30}\) kg).
17	Which symptoms are likely to afflict an astronaut in space: swollen feet, swollen face, headache, or orientational problems?	Swollen face, headache, and orientational problems are likely (due to upward fluid shift in microgravity); swollen feet are not.
18	A rocket is fired from Earth towards the Sun. At what distance from Earth's centre is the gravitational force on it zero? (\(M_{sun}=2\times10^{30}\) kg, \(M_{Earth}=6\times10^{24}\) kg, orbital radius \(=1.5\times10^{11}\) m)	≈ 2.6 × 10⁸ m from Earth's centre.
19	Mars orbits the Sun at about 4 times Mercury's orbital radius, and a Martian year is 687 Earth days. Using Kepler's third law, estimate Mercury's orbital period.	\( T_{Mercury} = 687/4^{3/2} = 687/8 \approx 85.9 \) days. (NEET 2025)
20	If the Sun's mass were reduced to one-tenth while G were increased ten-fold, would Earth's orbital period around the Sun or the acceleration due to gravity g on Earth's surface change?	Earth's orbital period stays the same (\(GM_{sun}\) is unchanged, so Kepler's third law gives the same T), but g on Earth's surface becomes 10 times larger (\(g=GM_E/R_E^2\) depends on G and Earth's own mass, not the Sun's). (NEET 2018)
21	A body weighs 200 N on Earth's surface. What is its weight halfway to the Earth's centre?	100 N, from \( g(d)=g(1-d/R_E)=g/2 \) at \(d=R_E/2\). (NEET 2019)
22	How does the gravitational field intensity vary with distance from the centre of a uniform solid Earth, from the centre outward?	It increases linearly from zero at the centre to a maximum at the surface, then decreases as \(1/r^2\) outside. (AIPMT 2014)
23	Two point masses m and 9m are separated by distance d. At what distance from m does the gravitational field vanish, and what is the gravitational potential there?	At \( x = d/4 \) from m; potential \( V = -16Gm/d \) (found using \(F=Gm_1m_2/r^2\) for the null point and \(V=-Gm/r\) with superposition). (NEET 2023)
24	Earth's escape speed is 11.2 km/s. A body is projected with speed 22.4 km/s. What is its speed far from Earth?	\( 11.2\sqrt{3} \approx 19.4 \) km/s, from \( V_f^2=V_i^2-V_{esc}^2 \). (NEET 2023, Manipur)
25	What is the orbital radius of a geostationary satellite (T=24 h), using \(M_E=6.0\times10^{24}\) kg and \(G=6.67\times10^{-11}\) N m² kg⁻²?	≈ 4.23 × 10⁷ m (about 42,000 km), from \( T^2=4\pi^2 r^3/(GM_E) \). (AIPMT 1992)