Free Gravitation MCQs with Answers

31. The two moving particles collide and clump together on a smooth horizontal surface. The following statements are given below:

• A. (a) and (c) are correct.
• B. (b) and (c) are correct.
• C. (a) and (d) are correct.
• D. (b) and (d) are correct.

Explanation: The following is the solution: B's statement is correct. In an isolated system, where no external forces are acting, the total energy of the system is conserved. This includes all forms of energy, such as kinetic energy, potential energy, and any other forms present in the system. During the collision and clumping process, if there are no external forces or energy losses to other forms (such as heat or sound), the total energy of the system will remain constant. D's statement is also correct. Since the particles are clumping together on a smooth horizontal surface, no external force is doing work on the system. However, as the particles come together and form a single clumped object, there is an internal force acting between them that brings them closer. Since this force acts in the opposite direction to the displacement, the work done by the system (the internal force) is negative. This negative work is equal in magnitude but opposite in sign to the positive work done by an external force in the opposite direction. It is obvious for the 2-mass system, whether it is elastic, inelastic, or perfectly elastic. The total energy of the system will remain conserved. But the final kinetic energy will be less than the initial K.E. So work done by the system will be negative.

32. A 2 kg body falls from infinity to the surface of earth. What will be the kinetic energy of the body on reaching the surface of Earth (Assume escape velocity to be 104 ms-1)?

• A. 108J
• B. 1016 J
• C. 1020 J
• D. 1024 J

Explanation: The following is the solution: Kinetic energy = 1/2 mvo2 = 1/2 x 2 (104)2 = 108 J

33. The weight of the body at the center of the Earth is:

• A. Zero
• B. Infinite
• C. Same as on the surface
• D. None of these

Explanation: The following is the solution: Because g at the center of the Earth is zero So weight = mg is also zero. This is because, at the center, the gravitational forces from all directions cancel each other out, resulting in a net gravitational force of zero.

34. When you move from the equator to the poles, the value of acceleration due to gravity (g):

• A. Increases
• B. Decreases
• C. Remains the same
• D. Increases then decreases

Explanation: This is the following solution: From the equation: g'=g - ω2 Re cos2λ Where λ is the latitude which is 0° at the equator and 90° at the poles. As you move from the equator to the pole, the value of acceleration due to gravity (g) increases. This is because the Earth is not a perfect sphere but slightly flattened at the poles, which results in a greater distance from the Earth's center at the equator. According to the law of universal gravitation, the gravitational force is inversely proportional to the square of the distance, so the force of gravity is stronger at the poles than at the equator.

35. Average density of the Earth:

• A. Is directly proportional to g
• B. Is inversely proportional to g
• C. Does not depend on g
• D. Is a complex function of g

Explanation: The following is the solution: The gravitational constant g is given as: g=GM/R2 Density D=mass/volume =g×R2/G×Ve (Where Ve is the volume of the earth ) D=g×R2/ G×3/ 4 πR3 =3g/4πGR Hence, D∝g.

36. The binding energy of a particle of mass m with a planet, when it is on the planet's surface, is 1/2mv02. A tunnel is dug along the diameter of the planet and the particle is dropped into it from the surface, when the body reaches the center of the planet, its speed is:

• A. v0
• B. v0/√ 2
• C. Zero
• D. V0/2

Explanation: This is the following solution: The motion of the particle within the tunnel is simple harmonic. At the mean position, all of its energy is K.E. which is equal to half of binding energy.

37. Force of gravitation is directly proportional to the product of _

• A. Masses
• B. Volumes
• C. Weights
• D. Surface areas

Explanation: According to Newton's law of universal gravitation, the force of gravitation between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

38. Gravitational force is inversely proportional to_the two bodies:

• A. Distance between
• B. Square of the distance between
• C. Product of the masses
• D. None of the above

Explanation: According to Newton's law of universal gravitation, the force of gravitation between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

39. Gravitational force can be considered as a:

• A. Fictitious force
• B. Universal force
• C. Pair of action and reaction forces
• D. Dragging force

Explanation: Gravitational force is a fundamental force of nature that acts universally between all objects with mass. It is described by Sir Isaac Newton's law of universal gravitation, which states that every point mass attracts every other point mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

40. The value of G was found by:

• A. Cavendish
• B. Newton
• C. Michelson
• D. Watt

Explanation: The value of the gravitational constant G was determined by the physicist Henry Cavendish through his famous Cavendish experiment, which he conducted in 1797-1798.