Gravitation — Set 1
Physics · गुरुत्वाकर्षण · Questions 1–10 of 60
Newton’s law of gravitation states that the force between two point masses is proportional to which combination?
Correct Answer: B. Product of the two masses and inversely proportional to the square of the distance
Gravitational force depends on m1×m2 and 1/r^2. This is the inverse square law of gravitation. It acts along the line joining the two masses.
What is the dimensional formula of the universal gravitational constant G?
Correct Answer: A. [M^-1 L^3 T^-2]
From F = G m1 m2 / r^2, G = Fr^2/(m1m2). So its dimensions are [M^-1 L^3 T^-2]. This remains the same in all unit systems.
Which statement correctly relates mass and weight of a body near Earth?
Correct Answer: A. Weight equals mg and changes if g changes
Weight is the gravitational force and equals mg. If g changes with place, weight changes too. Mass is the amount of matter and stays the same.
The expression for escape velocity from the surface of a planet of mass M and radius R is?
Correct Answer: B. sqrt(2GM/R)
Escape velocity is the minimum speed to reach infinity with zero final speed. It is found by equating kinetic energy to gravitational potential energy change. The formula is v = sqrt(2GM/R).
If h is small compared to Earth’s radius R, the acceleration due to gravity at height h is best approximated by?
Correct Answer: B. g
Gravity decreases with altitude because distance from Earth’s center increases. For small h, g' ≈ g(1 - 2h/R). This comes from g' = g(R/(R+h))^2 using binomial approximation.
The gravitational potential V at a distance r from a point mass M (taking V = 0 at infinity) is?
Correct Answer: B. -GM/r
Gravitational potential is work done per unit mass in bringing a test mass from infinity. For a point mass, it is negative and equals -GM/r. The negative sign shows the force is attractive.
What is the gravitational field inside a hollow spherical shell of uniform mass distribution?
Correct Answer: A. It is zero everywhere inside
Inside a uniform spherical shell, the net gravitational pull cancels out. So the gravitational field is zero at every interior point. This is a standard result of spherical symmetry.
How is gravitational field strength g related to gravitational potential V in the radial direction?
Correct Answer: B. g = -dV/dr
Field strength is the negative gradient of potential. Along radius, g = -dV/dr. The minus sign means field points toward decreasing potential.
For a conservative force like gravity, the work done over a closed path is?
Correct Answer: A. Zero
Gravity is a conservative force. Work done depends only on initial and final positions. Therefore, over a closed path the net work is zero.
Kepler’s third law of planetary motion states that?
Correct Answer: C. T^2 is proportional to r^3 for planetary orbits
The correct answer is 'T^2 is proportional to r^3 for planetary orbits'. Kepler’s third law links orbital period and orbit size. It says T^2 ∝ r^3 for bodies orbiting the same central mass. This is consistent with Newtonian gravitation.