Free Gravitation MCQs with Answers

91. Assuming the earth to be a uniform sphere rotating about an axis through the poles, the weight of a body at equator compared with its weight at the pole would be:

• A. Greater
• B. Smaller
• C. Equal
• D. None of these

Explanation: If we consider the Earth to be a perfect sphere (ignoring its actual oblate spheroid shape), the weight of a body at the equator would be slightly more than its weight at the pole. This is due to the centripetal acceleration caused by the Earth's rotation. At the equator, a point on the Earth's surface is moving faster in its rotation than a point at the poles. The centripetal acceleration needed to keep an object moving in a circle is given by: ac= v2/r where: - ac is the centripetal acceleration, - v is the linear velocity (speed) of the object, and - r is the radius of the circle (distance from the center of the Earth).

92. An ice-skater can greatly increase his speed of rotation in a spin by drawing in his limbs towards the spin axis. This is because:

• A. His moment of inertia decreases
• B. His angular momentum increases
• C. His potential energy decreases
• D. His centre of gravity changes

Explanation: We make use of the principle of conservation of angular momentum for this question. When the ice skater pulls in their limbs during a spin, their moment of inertia decreases due to the redistribution of mass. According to the conservation of angular momentum, as the moment of inertia decreases, the angular velocity (spin speed) must increase to maintain the same angular momentum. This principle is analogous to a figure skater spinning faster when pulling their arms and legs closer to their body.

93. If M is the mass and R is the radius of the earth, then which one of the following equations correctly relates the universal gravitational constant G to the acceleration of free fall g at the surface of the Earth?

• A. Option A
• B. Option B
• C. Option C
• D. Option D

Explanation: Option C is correct as it is the appropriate rearrangement of the formula.

94. The value of "g":

• A. Decreases with altitude
• B. Increases with altitude
• C. Is constant every where
• D. Does not depend upon altitude

Explanation: g= GM/R2 where R is the distance from the center of the earth. g is inversely proportional to the square of R and therefore with increase in R, g decreases.

95. The value of "g" _ with increase of the distance of the body from the centre of the earth:

• A. Increase
• B. Remain same
• C. Decrease
• D. Becomes twice

Explanation: g= GM/R2 where R is the distance from the center of the earth. g is inversely proportional to the square of R and therefore with increase in R, g decreases.

96. The gravitational forces acting on the two bodies form:

• A. Couple
• B. Reaction force
• C. Both couple and reaction pair
• D. An action and reaction pair

Explanation: According to Newton's third law of motion, for every action, there is an equal and opposite reaction. In the context of gravitational forces between two bodies, the gravitational force exerted by one body on another forms an action-reaction pair. Specifically, if Body A exerts a gravitational force on Body B, then Body B simultaneously exerts an equal and opposite gravitational force on Body A. Mathematically, if FAB is the gravitational force exerted by Body A on Body B, then FBA, the force exerted by Body B on Body A, is equal in magnitude but opposite in direction: FAB= -FBA These action-reaction pairs ensure that the forces are balanced and consistent with the conservation of momentum. Gravitational forces are always attractive and act along the line joining the centers of the two masses involved.

97. The main aim of Cavendish experiment was to obtain the measurement of:

• A. Acceleration due to gravity
• B. Inertia mass of a spherical body
• C. Tensional constant of small fibbers
• D. The value of universal gravitational

Explanation: The main aim of the Cavendish experiment, conducted by British scientist Henry Cavendish in 1797-1798, was to measure the mass of the Earth. Cavendish's experiment is famous for its determination of the gravitational constant often denoted as ( G ) and the mass of the Earth. In the experiment, Cavendish used a torsion balance, which consisted of a horizontal bar suspended from a thin wire. Two small lead spheres were fixed at each end of the bar, and two larger lead spheres were placed near the smaller ones. The gravitational attraction between the smaller and larger spheres caused a tiny twisting motion of the bar, allowing Cavendish to measure the torque and, consequently, determine the gravitational force between the masses. The Cavendish experiment provided a method for measuring the gravitational constant, which is a fundamental constant in Newton's law of universal gravitation. The gravitational constant relates the force between two masses to the product of the masses and the distance between their centers. By determining ( G ), Cavendish was able to indirectly calculate the mass of the Earth.

98. The value of gravitational constant "G" was found by means of:

• A. Newton's laws of motion
• B. Newton's law of gravitation
• C. Kepler's law
• D. Cavendish apparatus

Explanation: The main aim of the Cavendish experiment, conducted by British scientist Henry Cavendish in 1797-1798, was to measure the mass of the Earth. Cavendish's experiment is famous for its determination of the gravitational constant often denoted as ( G ) and the mass of the Earth. In the experiment, Cavendish used a torsion balance, which consisted of a horizontal bar suspended from a thin wire. Two small lead spheres were fixed at each end of the bar, and two larger lead spheres were placed near the smaller ones. The gravitational attraction between the smaller and larger spheres caused a tiny twisting motion of the bar, allowing Cavendish to measure the torque and, consequently, determine the gravitational force between the masses. The Cavendish experiment provided a method for measuring the gravitational constant, which is a fundamental constant in Newton's law of universal gravitation. The gravitational constant relates the force between two masses to the product of the masses and the distance between their centers. By determining ( G ), Cavendish was able to indirectly calculate the mass of the Earth.

99. Numerical value of "G" can also be estimated by knowing the_:

• A. Circular motion
• B. Mass of earth
• C. Average density of the air
• D. Weight of the earth

Explanation: Option B is correct as putting the values of the mass of earth m, the gravitational force F, and the distance from the center of the earth R, we can accurately calculate the value of the Gravitational constant (6.67 x 10-11 Nm2/Kg2)

100. If the distance between two bodies is doubled the gravitational force between them becomes:

• A. Half of the original value
• B. One third of the original value
• C. Doubled
• D. One fourth of the original value

Explanation: According to Newton's law of universal gravitation, the force of gravity between two objects is inversely proportional to the square of the distance between their centers. If the distance between two bodies is doubled, the gravitational force between them becomes one-fourth of the original force. This is because the force is inversely proportional to the square of the distance. So, if you double the distance between two bodies, the gravitational force between them decreases to one-fourth of its original value.