Team Quanta gladly presents all possible short questions of BS Physics book Mechanics – II’s Chapter#03: Gravitation for the students.
Q.1 Two planets are never seen at midnight. Which ones and why not? Can this be considered as evidence in favor of the heliocentric and against the geometric theory?
Answer: mercury and Venus are two planets which can never be seen at midnight because they are closer to sun than we are. So anything that is closer to sun is below horizon and not visible. This is considered to be in favor of heliocentric and against the geometric theory.
Q.2 If forces of gravity act on all bodies in proportion to their masses. Why does a heavy body not fall correspondingly faster than a light body?
Answer: Force of gravity depends on mass of body but there is an inverse relation between force of gravity and acceleration of body, so massive body moves with same acceleration as that of light body.
Q.3 Would we have more sugar to the pound at the poles or at the equator? What about sugar to the kilogram?
Answer: The weight of a pound is slightly less at the equator because the acceleration due to centrifugal force subtracts a small amount from the acceleration due to gravity so there is a little more sugar for a pound at equator. Sugar to kilogram: it would be same at either place.
Q.4 How can you determine mass of moon?
Answer: We can determine the mass of moon with the help of gravitational pull exerted on a satellite revolving around it which is firstly determined by distance and orbital speed of satellite. We can also determine mass of moon by kepler ’s 3rd law.
Q.5 The gravitational force exerted by the sun on the moon is about twice as great as the gravitational force exerted by the earth on the moon. Why then does the moon not escape from the earth?
Answer: The moon does not escape from earth because gravitational force exerted by earth on moon is equal to centripetal force.
Q.6 Explain why an object, orbiting around the earth, is said to be freely falling. Use your explanation to point out why objects appear weightless under certain circumstances?
Answer: When an object is thrown fast enough parallel to the earth, curvature of its path will match the curvature of earth then spaceship simply circle the earth. The object comes down with acceleration of gravity; hence we can say that the orbiting body is falling freely.
Q.7 What is effect of mass of satellite on its orbital speed?
Answer: Orbital speed of satellite is given by relation,
$$v=\ \frac{GM}{R+H}$$
Here M is the mass of earth. Above equation shows that orbital speed of satellite is independent of mass of satellite.
Q.8 The earth’s orbit is slightly elliptical. Earth is closer to sun during the northern hemisphere winter than it is during summer. Is speed of earth during winder same as its speed during summer?
Answer: In winter distance from sun to earth is less than it in summer. According to kepler’s 2nd law, the area swept by earth per month is same in winter and summer. Therefore, earth must move rapidly in winter. Thus speed of earth during winter is larger than in summer.
Q.9 Is the escape speed of 100N rocket less than the escape speed of 10,000N rocket?
Answer: Escape speed is given by relation,
$$V_{esc}=\ \sqrt{2gR}$$
This equation shows that escape speed is independent of weight of rocket have some escape speed.
Q.10 It is often said that astronauts in orbit experience weightlessness because they are beyond the pull of earth’s gravity. Is this statement is correct?
Answer: This statement is incorrect because astronauts experience weightlessness due to constant free fall.
Q.11 Saturn is about six axis times farther from the sun than Mars. Which planet has (a)- the greater period of revolution (b)- the greater orbital speed and (c)- the greater angular speed?
Answer: Because Saturn is farther from sun than Mars, it has greater period of revolution, less orbital speed and angular speed.
Q.12 Two masses of m and M are situated in air and gravitational force between them is F. The space around masses is now filled with a liquid of specific gravity 3. How gravitational force is affected?
Answer: There is no effect on gravitational force because gravitational force is independent of medium.
Q.13 Why can we learn more about the shape of the earth by studying motion of the artificial satellite than by studying the motion of moon?
Answer: As sun exerts force on moon so it is difficult to study the shape of earth but satellite are put in orbit of earth, that is why we can measure shape of earth easily.
Q.14 If you light a candle on space shuttle, would it burn the same as on earth?
Answer: No, it will not burn since there is no oxygen in space. However a small flame can be maintained in a controlled experiment for some time which will be spherical in shape.
Q.15 Would you expect the total energy of the solar system to be constant? Is the total angular momentum constant? Explain your answers.
Answer: Yes, total energy and angular momentum of in planetary motion are constant because these quantities are constants of motion.
Q.16 Suppose the earth were to suddenly shrink to half its current diameter, with its mass remaining constant. Would the escape speed of earth increase?
Answer: Yes, in this case the rockets starts closer to center of earth and therefore large speed is required to overcome the increased force of attraction.
Q.17 Does the radius vector of Mars sweep out same amount of area per unit time as that of earth? If not, why? If yes, prove it.
Answer: No, according to kepler’s 2nd law of planetary motion, area swept by a given planet per unit time is constant, whereas area swept out per unit time is different for each planet.
Q.18 A satellite in earth orbit experiences a small drag force as it starts to enter the earth’s atmosphere. What happens to its speed?
Answer: According to Newton’s 2nd law of motion,
F=ma
If the drag force reduces, deceleration would occur thus reducing its speed.
Q.19 A satellite goes through one complete orbit of earth. Is net work done on it by earth’s gravitational force positive or negative?
Answer: A satellite can coast in a stable orbit in a plane not passing through the earth’s center as the center of earth may not be center of mass exactly for a particular orbit.
Q.20 When moon is a new position directly between earth and sun, is net force exerted on it by sun and earth directed towards sun? Justify.
Answer: Yes, because sun exerts more force on moon than does on earth.
Q.21 Inside a spaceship, what difficulties would you encounter in walking, in jumping and drinking?
Answer: Walking, jumping and drinking is spaceship is difficult due to absence of gravity. The moment when force is exerted to walk or to jump, there is force to stop you and drinking in an open vessel or glass is not possible because we cannot pour it in the absence of gravity force.
Q.22 Why acceleration due to gravity near polar region is greater than that at the equatorial?
Answer: We know that,
$$g=\ \frac{GM\ \ }{R^2}$$
Earth is flattened at the poles. Thus polar radius is less than equatorial radius. Hence value of g is greater at poles than at equator.
Q.23 What value of work is done in moving an object of 50kg from one point to another on the surface of spherical shell?
Answer: The surface of the spherical shell is an equipotential surface. Hence no work is done in moving an object from one point to another on surface of spherical shell.
Q.24 How could you determine whether two objects have (a)-the same gravitational mass, (b)- the same inertial mass and (c)-the same weight?
Answer: If we know acceleration of body, then we can determine the gravitational mass, inertial mass and weight as all these quantities depend on acceleration and we can find acceleration from Newton’s law of gravitation.
Q.25 Two objects experience a gravitational attraction. Explain why gravitational force between them does not depend on sum of their masses.
Answer: According to Newton’s law of gravitation,
$$F=\ \frac{Gm_1m_2}{r^2}$$
The gravitational force does not include sum of masses of objects. Moreover if force of gravitation depends on sum of masses, then it can be predicted that there is a non- zero force even when one mass is zero which is physically impossible.
Q.26 Can we regard gravity as “fictitious” force arising from the acceleration of one’s reference frame relative to an inertial reference frame , rather than a “real” force?
Answer: The term gravity is real due to fact that things fall and have weight but force of gravity is a fictitious force as it involves a constant acceleration like fictitious forces.
Q.27 Two bodies on surface of earth do not move towards each other due to the force of attraction by Newton’s law of gravitation. Why?
Answer: The masses involved are small, so forces of attraction is very small to cause any acceleration. For example two masses each of 1kg separated by a distance of 1m have force of attraction of magnitude , which is too small to be felt.
Q.28 What is main drawback of Newton’s view about gravitation?
Answer: Newton was unable to justify the inverse square law because according to him space time is not curve but a straight.
Q.29 When a student passes his friend in the college, he does not feel gravitational force. Why?
Answer: When a student passing his friend in college exerts gravitational force on friend, but it is so small that cannot be felt.
Q.30 The force exerted by sun on moon is more than twice the force exerted by earth on moon. Should the moon be thought of as orbiting the earth or sun?
Answer: Moon can be thought of as orbiting the sun because the earth providing a smaller force makes the moon moving back and forth in its solar orbit.
Q.31 Out of four quantities speed, angular speed, kinetic energy and angular momentum, which one remains constant in planetary motion?
Answer: Angular momentum is conserved as there is no external torque.
Q.32 At what position in its elliptical orbit is the speed of a planet maximum or minimum?
Answer: By law of conservation of momentum , the speed of the planet is maximum at closest approach ( perihelion) and speed is minimum at farthest distance ( aphelion).
Q.33 An object of mass m is located on the surface of a spherical planet of mass M and radius R, then how escape speed from the planet vary with m?
Answer: Escape speed is given by,
$$V_{esc}=\sqrt{\frac{GM}{R}}$$
This relation show that escape speed is independent of mass m, so there is no change in escape velocity with variation of m.
Q.34 If a hole could be dug to the center of the earth, would the force on an object of mass m still obey Newton’s law of gravitation? What do you think the force on m would be at the center of the earth?
Answer: If the object is at the very center of the earth, then Newton’s law of gravitation does not apply. If there is a distance between object and center of Earth, then Newton’s law of gravitation can be applied. No, the gravitational force of the earth on an object at its center must be zero.
Q.35 A satellite in low Earth orbit is not truly travelling through vacuum. Rather, it moves through very thin air. Does the resulting air friction cause the satellite to slow down?
Answer: Air resistance cause a decrease in the energy of the Earth-satellite system. This reduces the radius of the orbit, due to which satellite must travel faster and hence the effect of air resistance increases the speed of light.
Q.36 Two forces of identical mass m and radius R are separated by 3R from their centers. How force of attraction is related to R?
Answer: By Newton’s law of Gravitation,
$$F=\frac{Gmm}{{(3R)}^2}=\ \ F=\frac{G\left(\frac{4\ \ \ }{3}\pi R^3\right)\left(\frac{4\ \ \ }{3}\pi R^3\right)}{{(3R)}^2}\ \propto\frac{1}{R^4}$$
Q.37 In his 1789 experiment, Cavendish was said to have “massed” the Earth.” What is meant by this statement?
Answer: Cavendish found G from his experiment, using this value of G, mass of earth can be determined by relation,
$$g=\ \frac{GM_E}{R_E^2}\ \rightarrow\ M_E=\ \frac{gR_E^2}{G}$$
Q.38 Explain why the force exerted on a particle by a uniform sphere must be directed toward the center of the sphere. Would this statement be true if the mass distribution of the sphere were not spherically symmetric?
Answer: Otherwise the components of the gravitational force perpendicular to the axis will not cancel. If the mass is not uniformly distributed the center of mass of the non uniform sphere will not lie along the axis.
Q.39 You are given the mass and radius of planet Y. How would you calculate the free fall acceleration on surface of this planet?
Answer: Free fall acceleration is determined by Newton’s second lae of motion,
$$a=\ \frac{F}{m}=\ \frac{\frac{GM_\gamma m}{R_\gamma^2}}{m}=\frac{GM_\gamma}{R_\gamma^2}$$
Q.40 Explain why it takes more fuel or a spacecraft to travel from the earth to moon than for the return trip. Estimate the difference.
Answer: Escape speed from the Earth = 1120m/s
Escape speed from the moon = 230 m/s
The fuel required is 25 times more fuel is to leave the Earth versus leaving the Moon.
Q.41 A satellite originally moves in a circular orbit of radius R around the earth? Suppose it is moved into a circular orbit of radius 4r. What does the force exerted on the satellite then become?
Answer: According to the inverse square law,
$F\propto\frac{1}{r^2}\ For\ \ r^\prime=4r$ we have $F^\prime\propto\frac{1}{16r^2}\rightarrow\ \frac{F^\prime}{F}=\ \frac{1}{16}$
Q.42 The gravitational force is exerted on an astronaut on the Earth’s surface is 650N directed downward. When he is in the space station in orbit around the earth, is the gravitational force on him zero?
Answer: No, the international space station orbits just above the atmosphere, gravitational force on the astronaut is slightly less than on the ground.
Q.43A satellite originally moves in a circular orbit of radius R around the earth? Suppose it is moved into a circular orbit of radius 4r.What happens to the satellite’s speed?
Answer: For a satellite moving in a circular orbit under gravitational force, we have
$$\frac{mv^2}{r}=\ \frac{GMm\ \ }{r^2}\rightarrow\ \ v\propto\frac{1\ }{\sqrt r}\ \ \ For\ \ r^\prime=4r,\ we\ have\ \ v^\prime\propto\frac{1}{\sqrt4}=\frac{1}{2}$$
Q.44 Imagine that a nitrogen and other atmospheric gasses were more soluble in water so that the atmosphere of the earth is entirely absorbed by the oceans. Atmospheric pressure would then be zero, and outer space would start at the planet’s surface. Would the Earth then have a gravitational field?
Answer: Yes, and it would be essentially the same as the current value since switching off the atmosphere has no effect on the planet’s gravitational field.
Q.45 A satellite moves in a circle orbit at a constant speed around the earth, then whether the satellite has an acceleration directed toward the Earth.
Answer: Yes, since the satellite experiences a gravitational force, always directed toward the center of its orbit, and supplying the centripetal force required to hold in its orbit.
Q.46 A satellite originally moves in a circular orbit of radius R around the earth? Suppose it is moved into a circular orbit of radius 4r.What happens to its period?
Answer: According to Kepler’s third law of planetary motion, period becomes eight times larger.
$$T^2=\ r^3\rightarrow T\propto \sqrt{r^3}\rightarrow T^\prime\propto 4^\frac{3}{2}=8\$$
