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Q 01 / 25
Gravitation is a force of attraction that acts between any two material objects in the universe.
Q 02 / 25
The gravitational constant \(G\) has the same value at all places in the universe.
Q 03 / 25
The value of acceleration due to gravity \(g\) is exactly the same at all points on the earth’s surface.
Q 04 / 25
The gravitational force between two point masses becomes one-fourth if the distance between them is doubled.
Q 05 / 25
The gravitational force between two bodies becomes zero if the distance between them becomes very large.
Q 06 / 25
For a spherically symmetric body, the gravitational field outside it is the same as if all its mass were concentrated at its centre.
Q 07 / 25
A spherically symmetric thin shell of mass exerts zero net gravitational force on a particle placed anywhere inside it.
Q 08 / 25
The gravitational potential at infinity is conventionally taken as zero.
Q 09 / 25
Gravitational potential is always positive for an attractive inverse-square law force like Newtonian gravity.
Q 10 / 25
The gravitational potential energy of a two-mass system becomes less negative as the distance between the masses increases.
Q 11 / 25
The acceleration due to gravity at a height \(h\) above earth’s surface is always greater than the value at the surface.
Q 12 / 25
Deep inside a uniform earth, the value of \(g\) decreases linearly with depth from the surface towards the centre.
Q 13 / 25
In a circular orbit around earth, the gravitational force on a satellite provides the necessary centripetal force.
Q 14 / 25
The orbital speed of a satellite in a circular orbit around earth increases with the radius of its orbit.
Q 15 / 25
The time period of a satellite in a circular orbit around earth increases as the radius of the orbit increases.
Q 16 / 25
Two satellites of different masses in the same circular orbit around earth must have the same orbital period.
Q 17 / 25
The escape speed from earth’s surface depends on the mass of the object being projected.
Q 18 / 25
A satellite in a stable circular orbit around earth is completely weightless because the gravitational force on it is zero.
Q 19 / 25
For a given central mass, the areal velocity of a planet in orbit remains constant if only gravitational force acts.
Q 20 / 25
If the distance between earth and sun became half, the orbital period of earth would become one-fourth of its present value.
Q 21 / 25
For a planet moving in an elliptical orbit, its total mechanical energy remains constant in the absence of non-gravitational forces.
Q 22 / 25
The gravitational field between two equal point masses placed at a finite separation is zero at exactly one point on the line joining them.
Q 23 / 25
Inside a planet of uniform density, the gravitational potential is maximum (least negative) at the centre.
Q 24 / 25
For a satellite in a circular orbit, the total energy is numerically equal to its gravitational potential energy.
Q 25 / 25
In a two-body system interacting only via Newtonian gravitation, the motion can be reduced to that of a single body of reduced mass moving in an effective central potential.

Frequently Asked Questions

Gravitation is the universal force of attraction acting between all bodies with mass, keeping objects grounded and governing planetary motion.

Every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them: \( F = G \frac{m_1 m_2}{r^2} \), where \( G = 6.67 \times 10^{-11} \, \mathrm{N \, m^2 \, kg^{-2}} \).

(1) Law of Orbits: Planets move in elliptical orbits with the Sun at one focus. (2) Law of Areas: The line from Sun to planet sweeps equal areas in equal times. (3) Law of Periods: \( T^2 \propto a^3 \), where \( T \) is orbital period and \( a \) is semi-major axis.

\( g = \frac{GM_E}{R_E^2} \approx 9.8 \, \mathrm{m/s^2} \), where \( M_E \) is Earth's mass and \( R_E \) is Earth's radius.

\( g_h = g \left(1 - \frac{2h}{R_E}\right) \) for \( h \ll R_E \); more generally \( g_h = \frac{GM_E}{(R_E + h)^2} \).

\( g_d = g \left(1 - \frac{d}{R_E}\right) \).

For two masses, \( U = -\frac{G m_1 m_2}{r} \) (zero at infinity).

Minimum speed to escape Earth's gravity: \( v_e = \sqrt{\frac{2GM_E}{R_E}} = \sqrt{2g R_E} \approx 11.2 \, \mathrm{km/s} \).

\( v_o = \sqrt{\frac{GM_E}{r}} \), where \( r = R_E + h \); relates to escape speed by \( v_e = \sqrt{2} v_o \).

Work done by gravity is path-independent, allowing definition of potential energy and conservation of mechanical energy in the gravitational field.

Force per unit mass: \( \vec{g} = -\frac{GM}{r^2} \hat{r} \); scalar potential \( V = -\frac{GM}{r} \).

Both satellite and occupants are in free fall toward Earth with the same acceleration, so no normal reaction is exerted on the body.

A satellite in circular equatorial orbit with time period \( T = 24 \,\text{h} \) at height \( h \approx 36{,}000 \,\text{km} \) that appears fixed over one point on Earth.

For a satellite very close to Earth’s surface, \( T_0 = 2\pi \sqrt{\frac{R_E}{g}} \approx 85 \,\text{min} \).

The gravitational force becomes \( \frac{1}{9} \) of the original, because \( F \propto \frac{1}{r^2} \).
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