Gravitation — Set 2
Physics · गुरुत्वाकर्षण · Questions 11–20 of 60
The orbital speed v of a satellite in a circular orbit of radius r around a planet of mass M is?
Correct Answer: B. sqrt(GM/r)
In a circular orbit, gravity provides centripetal force. Setting GMm/r^2 = mv^2/r gives v = sqrt(GM/r). A larger orbit radius gives a smaller orbital speed.
The time period T of a satellite in a circular orbit of radius r around a planet of mass M is?
Correct Answer: B. 2π sqrt(r^3/GM)
Orbital period depends on orbit size and central mass. Using v = sqrt(GM/r) and T = 2πr/v gives T = 2π sqrt(r^3/GM). This is a form of Kepler’s third law.
Astronauts in an orbiting spacecraft feel weightless mainly because?
Correct Answer: D. They are in continuous free fall with the spacecraft
Gravity still acts strongly in low Earth orbit. Astronauts and the spacecraft fall together toward Earth. With no supporting normal force, they feel weightless.
For a uniform Earth, how does g vary with depth d below the surface (where d is small compared to R)?
Correct Answer: D. g decreases approximately as (1 - d/R)
Inside a uniform sphere, only the mass within radius contributes to gravity. That effective mass decreases with depth, so g reduces. For small d, g' ≈ g(1 - d/R).
The gravitational potential energy U of a mass m at distance r from a mass M (taking U = 0 at infinity) is?
Correct Answer: B. -GMm/r
Potential energy is m times gravitational potential. Since potential is -GM/r, U = m(-GM/r) = -GMm/r. The negative sign indicates a bound gravitational system.
If the distance between two masses is doubled, the gravitational force between them becomes?
Correct Answer: C. One-fourth
Gravitational force varies as 1/r^2. If r becomes 2r, then force becomes 1/(2^2) = 1/4. So it reduces to one-fourth of the original value.
Neglecting air resistance, the acceleration of a freely falling body near Earth is?
Correct Answer: D. Independent of its mass
In free fall, the force is mg and the mass is m, so acceleration is mg/m = g. Thus acceleration does not depend on the body’s mass. Differences in real life come mainly from air resistance.
For a uniform solid sphere, the gravitational field at the exact center is?
Correct Answer: D. Zero
At the center, pulls from all directions balance perfectly. So the net gravitational field is zero. Symmetry makes the resultant cancel out.
Which statement about gravitational potential energy of a satellite in a bound orbit is correct?
Correct Answer: D. It is negative
For a bound orbit, the reference at infinity makes gravitational potential energy negative. It equals -GMm/r for a circular orbit. Negative energy indicates the satellite is gravitationally bound.
A geostationary satellite must have which property?
Correct Answer: A. Its period is 24 hours and it orbits in the equatorial plane
A geostationary satellite appears fixed over one point on Earth. That requires the same rotational period as Earth, about 24 hours. It must orbit in the equatorial plane in the same direction as Earth’s rotation.