Free Gravitation MCQs with Answers

191. The gravitational acceleration is maximum on poles as compared to that on equator because:

• A. Distance between the poles and center of the earth is less as compared to that between the equator & center.
• B. Distance between the poles and the center of the earth is more as compared to that between the equator and center.
• C. The mass of the earth on the poles is greater as compared to that on the equator.
• D. The mass of the earth on the poles is less as compared to that on the equator.

Explanation: The correct option is: A) Distance between the poles and the center of the Earth is less as compared to that between the equator and center. The gravitational acceleration depends on both the mass of the Earth and the distance from the center of the Earth. The formula for gravitational acceleration is given by: g= GM/r 2 Option A is correct because the distance, r, in the gravitational acceleration formula, is the distance from the center of the Earth. The Earth is not a perfect sphere; it is slightly flattened at the poles and bulging at the equator due to its rotation. Therefore, the distance from the center of the Earth to the poles is less than the distance to the equator. Option B is incorrect because the distance between the poles and the center of the Earth is less. Option C and D are incorrect because the mass of the Earth is considered constant in this context, and the variation in gravitational acceleration is primarily due to the variation in distance from the center of the Earth.

192. An astronaut of weight, 'mg' is moving upwards in a rocket with an acceleration, '4g'. His apparent weight inside that rocket will be:

• A. zero
• B. mg
• C. 3 mg
• D. 5 mg

Explanation: The correct option is: D) 5 mg The apparent weight of an object is the force exerted by a supporting surface (such as a floor or a scale) on the object. In this case, the astronaut is moving upwards in a rocket with an acceleration of '4g'. The apparent weight (W') can be calculated using the following formula: W'=m ( g+a )----------------------- where w' is the apparent weight so W'=m x (g+4g) w'=5mg So, the apparent weight is 5 times the weight of the astronaut. Therefore, the apparent weight of the astronaut inside the rocket is 5mg and the correct option is D) 5 mg .

193. Free falling bodies:

• A. Have maximum weight
• B. Have minimum weight
• C. Have no weight
• D. Have any weight

Explanation: The correct option is: C) Have no weight When a body is in free fall, it accelerates under the influence of gravity, and during this period of free fall, it experiences weightlessness. Weight is the force with which gravity pulls an object toward the center of the Earth (or any other massive body). In free fall, the object is essentially in a state of continuous acceleration, and it is not resisting gravity. As a result, the normal force (which gives the sensation of weight) experienced by the object is zero, and it is effectively weightless.

194. A boy standing in a lift falling freely under gravity releases a ball from his hand. As seen by him the ball:

• A. Falls down
• B. Remains stationary
• C. Goes up
• D. None of the above

Explanation: The correct option is B) Remain stationary When the lift falls freely under gravity (in free fall), everything inside the lift, including the boy and the ball, accelerates at the same rate due to gravity. Since both the boy and the ball are accelerating downward at the same rate, they effectively remain in the same relative position within the lift. Therefore, as observed by the boy, the ball would appear to remain stationary in the air when released from his hand. Gravity is acting equally on both the boy and the ball, causing them to fall together, and the ball does not exhibit any relative motion with respect to the boy in this scenario.

195. A satellite moves in the circle orbit at the constant speed under the action of the gravitational force of a planet. The work done on the satellite in one revolution will have magnitude:

• A. Zero
• B. Half of the gravitational pull of the planet
• C. Equal to the gravitational pull of the planet
• D. Proportional to the diameter of the orbit

Explanation: A is the correct answer. In a circular orbit, the gravitational force is acting perpendicular to the direction of motion of the satellite. The work done by a force is given by the formula W= F ⋅ d, where F is the force, and d is the displacement. Since the gravitational force and the displacement are perpendicular, the dot product is zero, and the work done is zero.

196. A body in satellite orbiting round the earth is weightless because:

• A. It is essentially a freely falling body
• B. It is far away from the earth to experience the pull of the earth
• C. The moon attracts the body with a force equal to its weight
• D. None of the above

Explanation: A is the correct explanation. A body in orbit is essentially in free fall towards the Earth. The gravitational force from the Earth causes the body to accelerate, and if it has the right velocity, it will continuously fall around the Earth, creating an orbit. In this state of free fall, the gravitational force is balanced by the centripetal force required to keep it in orbit. This results in a continuous state of falling, creating a sensation of weightlessness for the body and everything inside it.

197. Artificial gravity can be created in the space craft by:

• A. Revolving it around the earth
• B. Spinning it around its own axis
• C. Increasing its velocity
• D. Decreasing its velocity

Explanation: B is a correct option. Centrifugal force due to rotation can simulate the effects of gravity. If a spacecraft is spinning around its own axis, the astronauts inside would experience a force pushing them toward the spacecraft's outer edges, simulating the feeling of gravity. This is similar to the artificial gravity seen in some sci-fi movies, like the spinning space station in "2001: A Space Odyssey."

198. When a man circles round the earth in a satellite, then:

• A. His mass becomes zero but weight remains constant
• B. His mass remains constant but weight becomes zero
• C. Both mass and weight remain constant
• D. Both mass and weight become zero

Explanation: B is more accurate. The person's mass remains constant because it is an intrinsic property, but their weight is effectively zero or significantly reduced. In orbit, the gravitational force acting on the person is balanced by the centripetal force required for orbital motion, creating a state of continuous free fall and weightlessness.

199. A space ship is coming towards earth from moon at a high speed. The speed of the air ship has to be reduced. A rocket is fired to lower its speed in a certain direction. The rocket should be fired:

• A. In the direction towards the earth
• B. In the direction towards the moon
• C. On the right side of space ship
• D. On the left side of space ship

Explanation: A is the correct answer. Firing the rocket in the direction towards the Earth, opposite to the motion of the spacecraft, will result in a deceleration, helping to reduce its speed.

200. The radius of Earth is 6 x 10^6m. What is the acceleration of a meteor, when it is 8 x 10^6m from the center of the Earth?

• A. 8 m/s2
• B. 4 m/s2
• C. 9.8 m/s2
• D. None of above

Explanation: The following is the solution: Law of Universal Gravitation states that the force of attraction FG between two bodies of masses M1 and M2 is directly proportional to the product of masses of the two bodies. it is also inversely proportional to the square of the distance r between the two. Mathematically stated: FG=GM1M2/r2 where G is the proportionality constant and =6.67408×10−11m3kg−1s−2 Let m be mass of meteor and Me mass of earth. Using Newton's second law of motion we can rewrite the equation as: FG=ma a=FG/m= GMe/r2 Inserting various values we get: a=6.3 ms-2