Q: Near Earth’s surface, acceleration due to gravity g is related to Earth’s mass M and radius R by?
Answer: g = GM/R^2
Explanation: Gravity at the surface is the field of a mass at distance R. Using g = GM/R^2 gives the correct dependence. Larger M increases g while larger R decreases g.
Q: For small heights h above Earth’s surface (h << R), the approximate relation for g at height h is?
Answer: g' ≈ g(1 - 2h/R)
Explanation: Gravity decreases with increasing distance from Earth’s center. Using g' = g(R/(R+h))^2 and expanding gives g' ≈ g(1 - 2h/R). This approximation works well when h is much smaller than R.
Q: Which statement about mass is correct?
Answer: Mass is measured in kilograms and does not depend on location
Explanation: Mass is the amount of matter in a body. Its SI unit is kilogram. It does not change with place even if gravity changes.
Q: Which statement about weight is correct?
Answer: Weight is measured in newtons and depends on g
Explanation: Weight is a force due to gravity. It equals mg, so it depends on local g. Its SI unit is newton.
Q: The time taken by Earth to complete one revolution around the Sun is approximately?
Answer: 365.25 days
Explanation: Earth’s orbital period defines one year. It is about 365.25 days. The extra quarter day leads to leap years.
Q: When two bodies attract each other gravitationally, the forces they exert are?
Answer: Equal in magnitude and opposite in direction
Explanation: Newton’s third law applies to gravitational forces. Each body pulls the other with equal magnitude. The directions are opposite along the line joining them.
Q: Escape velocity from a planet depends on?
Answer: The planet’s mass and radius, not the object’s mass
Explanation: Escape speed is v = sqrt(2GM/R). It depends on the planet’s mass M and radius R. The object’s mass cancels out in the energy equation.
Q: If the radius of a planet doubles while its mass stays the same, the escape velocity becomes?
Answer: 1/sqrt(2) times
Explanation: Escape velocity is v = sqrt(2GM/R). If R becomes 2R, then v becomes sqrt(1/2) of the old value. That is a decrease by a factor of 1/sqrt(2).
Q: Gravitational field lines around an isolated spherical mass are?
Answer: Radial and directed inward toward the mass
Explanation: Field lines show the direction of gravitational force on a test mass. Gravity attracts, so the lines point toward the mass. For spherical symmetry, the pattern is radial.
Q: The SI unit of gravitational potential (V) is?
Answer: J/kg
Explanation: Gravitational potential is potential energy per unit mass. So its unit is joule per kilogram. It is also equivalent to m^2/s^2 in SI.