Gravitation practice · Mixed difficulty

Option B (speed of galaxy) is correct because Hubble's law states that the recessional velocity of a galaxy is proportional to its distance from the observer.

The correct answer is B (Statement-1 is true, Statement-2 is false) because Earth is closer to the Sun in summer, and angular momentum is conserved.

Option B ($\frac{{9R}}{2}$) is correct because it is derived from equating the orbital speed to one-third of the escape speed and solving for the orbital radius.

Option B is correct because for a satellite in orbit, the kinetic energy is half the magnitude of the potential energy, and the potential energy is negative.

Option D (Each decreases at different rates) is correct because the gravitational field decreases differently inside and outside the Earth.

Option B (Decrease) is correct because the time period of a satellite is directly related to its orbital radius, so decreasing the radius decreases the time period.

Option A is correct because escape velocity is independent of the angle of projection.

Option D (Decrease by 89%) is correct because the gravitational force decreases inversely with the square of the distance, resulting in an 89% decrease when the distance triples.

Option A (${g_e} > {g_h} < {g_d}$) is correct because gravity decreases with height and depth, but the rate of decrease is different, with $g_h$ decreasing faster than $g_d$ for small h=d.

Option D (Both (1) and (2) are incorrect) is correct because when the radius of orbit decreases, kinetic energy increases and potential energy decreases.

Option B (Statement-1 is true, Statement-2 is false) is correct because the acceleration due to gravity becomes the same everywhere if the Earth stops rotating, and the value of g depends on the rotation of Earth.

Option B (22.4) is correct because the escape velocity is proportional to the square root of (M/R).

Option A (40 kg f) is correct because the weight on Mars is calculated using the ratio of gravitational accelerations on Mars and Earth.

Option C (The normal force is zero) is correct because the person and the chair are in free fall together, so there is no normal force exerted by the chair on the person.

Option A (Statement-1 is true, Statement-2 is true) is correct because the angular momentum of a planet is conserved due to the absence of external torque, while other parameters change due to the elliptical orbit.

Option C (Areal velocity) is correct because Kepler's Second Law states that a satellite's areal velocity remains constant in its orbit.

Option A ($K < |U|$) is correct. For a planet in an elliptical orbit, the magnitude of the potential energy is always greater than the kinetic energy.

Option B is correct. The average density of the Earth depends on g, but the reason given (density is mass/volume) is a true statement but not the correct explanation.

Option A ($1:4$) is correct because the ratio of kinetic energies is inversely proportional to the ratio of the masses.

Option D (Statement-1 is false, Statement-2 is true) is correct because the period is directly proportional to the radius and inversely proportional to the speed, but the relationship isn't a simple inverse proportionality due to the dependence of orbital speed on the radius.

Option C (Will not change at the poles) is correct because the effect of Earth's rotation on gravity is zero at the poles.

Option A ($5370 \mathrm{~s}$) is correct because it is the calculated period of revolution using the given radius of Earth, height of the satellite, and acceleration due to gravity.

Option A is correct because the work done to project a body to infinity is equal to the change in potential energy, which is mgR.

Option B (1:1) is correct because the period of revolution of a satellite depends only on the orbital radius and the mass of the planet, not the mass of the satellite.

Option B (Decrease at the equator but remain unchanged at the poles) is correct because the effective gravitational acceleration decreases at the equator due to the increased rotational speed, while it remains unchanged at the poles.

Option A ($\frac{S}{R}$) is correct because when the drops combine, the radius increases, and the pressure difference decreases.

Option B (If both assertion and reason are true but reason is not correct explanation of the assertion) is correct because while both statements are true, the reason doesn't explain why an astronaut experiences weightlessness.

Option A is correct because the gravitational field inside a hollow sphere is zero, leading to zero net force.

Option D is correct because a geostationary satellite orbits in the equatorial plane, maintaining a fixed position relative to Earth.

Option D ($20 \mathrm{~km}$) is correct because the depth at which the acceleration due to gravity is the same as at a height of 10 km is twice the height, assuming uniform mass density.