Gravitation practice · Easy

Option A (is maximum at the poles) is correct because the Earth is not a perfect sphere, and its radius is smaller at the poles than at the equator, leading to a higher value of g at the poles.

Option C ($11.2 \mathrm{~km} / \mathrm{sec}$) is correct because it is the approximate value of the escape velocity from Earth.

Option D ($M$) is correct because mass is an intrinsic property of an object and does not change with location.

Option C (Statement-1 is false, Statement-2 is true) is correct because the speed of a satellite varies in an elliptical orbit, and the speed does depend on the path.

Option B (The period of the satellite is nearly 129 days) is correct because it is calculated using Kepler's third law.

Option B ($V_P=2 V_E$) is correct because the escape velocity is directly proportional to the radius when the average mass-densities are equal.

Option C (Assertion is True, Reason is False) is correct because the gravitational potential at the surface of a solid sphere is less than at the center, but the potential inside the sphere is not constant.

Option B (mass of the satellite) is correct because the orbital velocity depends on the mass and radius of the Earth, and the gravitational constant, but not on the mass of the satellite.

Option B is correct because both the assertion and the reason are true, but the reason does not fully explain the assertion. The time period depends on height, but the given time is a known approximation for near-earth orbits.

Option C (E is always negative) is correct because the total energy of a planet in an elliptical orbit is always negative, indicating a bound system.

Option B is correct because the escape velocity depends on the mass of the Earth, the gravitational constant, and the point of projection relative to the Earth (radius), but not the mass of the projectile.

Option A (increases) is correct because the acceleration due to gravity (g) increases as you move from the equator to the poles due to the Earth's shape and rotation.

Option A ($g$ will decrease) is correct because $g$ is inversely proportional to the square of the radius, so increasing the radius decreases $g$.

Option A (Maximum) is correct because the value of 'g' is maximum at the poles due to the Earth's shape.

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 (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 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 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 B (55) is correct because the escape velocity is proportional to the square root of (mass/radius), and with the given changes, it becomes 5 times the Earth's escape velocity.

Option A (Statement-1 is true, Statement-2 is true) is correct because both the gravitational field intensity and the gravitational potential on the surface of a sphere are correctly stated.

Option D (If Assertion is incorrect but Reason is correct) is correct because the time period of a satellite depends on the mass of the earth, and shrinking the earth's radius would change the satellite's period.

Option B (7 R) is correct because a geostationary satellite is approximately 6R from the surface of the earth, hence 7R from the center.

Option A (Statement-1 is true, Statement-2 is true) is correct because gravitational force is conservative, leading to zero work in a closed loop and path independence.