Acceleration Due To Gravity - Conceptual Q & A Class - XI
1. By how much does the gravitational force between two objects decrease when distance between them is doubled?
Solution: According to Newton’s law of gravitation, gravitational force F is given by, F = GmM/r2. If the distance between the objects is doubled, the gravitational force between the objects decreases to 1/4th of the original force.
2. If there is an attraction force between all objects, why do we not feel ourselves gravitating towards massive buildings in our vicinity?
Solution: Gravity pulls us to massive buildings and everything else in the universe. The forces between us and the buildings are relatively small because masses are small compared to the mass of the earth. The forces due to stars are small because of their great distances. These tiny forces escape our notice when they are overwhelmed by the overpowering attraction to the earth.
3. Consider an apple at the top of a tree that is pulled by earth gravity with a force of 1 Newton. If the trees were twice as tall, would the force of gravity be 1/4th as strong?
Solution: No, because twice as tall tree is not twice as far from earth’s center. The trees height would have to be equal to radius of the earth (6370 km) before the force on the apple reduces to ¼ N. Before its weight reduces by 1%, the apple or any object must be raise 32 km above the surface of the earth, nearly 4 times the height of Mount Everest. So as a practical matter, we disregard the affects of everyday changes in elevation.
4. Which pulls with greater force on the oceans of the earth, the sun or moon?
Solution: The sun, but it is so distant that it attracts all parts of the earth with almost equal strength. Hence its effectiveness in raising tides is less than that of the moon.
5. The acceleration due to gravity is progressively less as we toward the center of the earth why?
Solution: As you move toward the earth you are also being pulled up by the part of the earth above you. When you are at center of the earth, the pull down is balance by the pull up so the g=0.
6. If you stepped into a hole bored clear through the center of the earth and made no attempt to grab the edges at either end, what kind of motion would you experience?
Solution: You would oscillate back and forth, in what is called simple harmonic motion (SHM). Each trip would take nearly 90 minutes.
7. Half way to the center of the earth, would you weigh more or weigh less than you weight at the surface of the earth?
Solution: You would weigh less because the part of the earth’s mass that pulls you down is counteracted by the mass above you pull up. If the density of the earth were uniform, halfway to the center of earth, your weight would weigh exactly half your weight at the surface of the earth. But since earth core is dense (about 7 times the density of the surface rock), your weight would be somewhat more than half surface weight. Exactly how much depends upon how earth’s density varies with depth information that is not known today.
8. A body is taken from the center of the earth to the moon. What will be the change in the weight of the body?
Solution: The weight of the body at the center of earth will be 0 (g=0). As the body is moved from the center to the earth surface, its weight will increase due to the increase in the value of the g. At the surface of the earth, the weight of the body will be maximum. As the body is moved above the surface of the earth, its weight will decrease due to decrease in the value of g. At one place where the gravitational force of the earth and moon are equal and opposite, the weight will become 0. Beyond this up to moon, gravitational force of the moon and hence the weight of the body will go on increasing.
9. The value of g on the moon is 1/6th of that on the earth. If the body is taken from earth to the moon, then what will be the change in its weight, inertial mass and the gravitational mass?
Solution: The weight of the body on the moon will be 1/6th of that on the earth. However there will be no change in the inertial or gravitational mass of that body.
10.The mass and diameter of a planet are twice those of the earth. What will be the time period of that pendulum on this planet which is a second pendulum on the earth?
Solution: The value of g = GM/R2.
If the mass and diameter are doubled, then g will reduce to half. Therefore,
the time period if a pendulum will be 
times to that on the earth. As a result
the time period of second’s pendulum of the earth will be 2 
seconds on the planet.
11.There is no effect of the rotational motion of the earth on the value of g at the poles. Why?
Solution: Acceleration due to gravity at a latitude is given by:g’ = g – R(ω cos λ )2. At the poles the value of λ is 90 deg. Hence in the formula g’ = g, so there is no effect of rotational motion of earth on the value of g at the poles.
The effect of rotation earth on the value of g is the greatest at the equator. Why?
Solution: This is because the value of λ at the equator will be zero deg. hence the cosine term will be maximum; the effect of rotation of earth on the value of g is greatest at the equator.
12.What are gravitation and gravity?
Solution: Gravitation is the force of attraction between any two bodies in the universe. However gravity is the force of attraction exerted by the earth towards its center on a body lying on or near the surface of earth. Note that gravity is merely a special case of gravitation.
13.The force of gravity acts on all bodies in proportion to their masses. Why does a heavier body not fall faster than a right light body?
Solution: This is due the fact that the value of acceleration due to gravity that is g, is independent of the mass of the body. Therefore, all masses fall with the same rapidity provided air resistance is neglected.
14.Why do two bodies of the same mass but different volumes not reach the earth simultaneously if the medium is air?
Solution: The upward thrust of air on a body with smaller volume will be less than that on the body with larger volume. Consequently, the body with smaller volume will reach the earth earlier.
15.Generally, the path of a projectile from the earth is parabolic but it is elliptical for projectiles going to a very great height. Why?
Solution: Near the earth surface, the value of g is essentially constant. Therefore, the projectile moves under a nearly uniform gravitational force and hence its path is parabolic. However at a very great height, the value of g decreases rapidly and a varying gravitational force acts on the projectile. Therefore the projectile path is elliptical.
