Q#11
The weight of the body at poles is greater than the weight at the equator. Is it the actual weight or the apparent weight we are talking about? Does your answer depend on whether only the earth’s rotation is taken into account or the flattening of the earth at the poles is also taken into account?Answer:
The weight at the equator is the apparent weight which is affected by the earth’s rotation and flattening of the earth at the poles. At poles, it is maximum and unaffected by these two reasons.
Q#12
If the radius of the earth decreases by 1% without changing its mass, will the acceleration due to gravity at the surface of the earth increase or decrease? If so by what percent?
Answer:
The mass of the earth can be considered concentrated at its center for calculation of the force between the earth and the object on or beyond its surface. With the mass of the earth being the same if the radius decreases by 1% it means the distance between the earth and the object reduces by 1%, other things being the same. Since the acceleration due to gravity is inversely proportional to the square of the radius of the earth R, the decrease in R will result in an increase in g.
The 1% decrease in R means it decreases by 0.99 times. So, the increase in g will be 1/(0.99)² = 1.02 times. That means the value of g increases by 2%.
Q#13
A nut becomes loose and gets detached from a satellite
revolving around the earth. Will it land on the earth? If yes, where will it land? If no, how can an astronaut make it land on the earth?
Answer:
No it will not land on the earth. It will orbit the earth like the satellite.
The astronaut will have to make its speed roughly towards the earth instead of the tangential speed.
Q#14
Is it necessary for the plane of the orbit of a satellite to pass through the center of the earth?
Answer:
Yes. Because the centripetal force on the satellite is towards the center of the earth where the earth’s mass is apparently considered to be concentrated.
Q#15
Consider earth satellites in circular orbits. A geostationary satellite must be at a height of about 36000 km from the earth’s surface. Will any satellite moving at this height be a geostationary satellite? Will any satellite moving at this height have a time period of 24 hours?
Answer:
No, only the satellites at this height moving over the equator and having the direction of rotation same as that of the earth will be geostationary and they will appear to be fixed at a place when viewed from the earth.
Yes, any satellite moving at this height will have the actual time period of 24 hours though this may not appear from the earth's surface depending upon their orbit and the direction of the rotation.
Q#16
No part of India is situated on the equator? Is it possible to have a geostationary satellite which always remains over New Delhi?
Answer: No.
Q#17
As the earth rotates about its axis, a person living in his house at the equator goes in a circular orbit of radius equal to the radius of the earth. Why does he/she not feel weightless as a satellite passenger does?
Answer:
To feel the weightlessness in a circular orbit around the earth, the person should orbit with such a speed so that the centrifugal force must be equal to the apparent weight of the person. For this condition g = v²/R at earth's surface. This gives,
v =√gR = √(9.8 x 6400000) = 7920 m/s = 7.92 km/s
So only going in the circular orbit at the surface of the earth is not sufficient for the weightlessness but his speed also should be 7.92 km/s which is not possible for a person even in a vehicle or plane. Also, the resistance of air on the surface will make the vehicle burn at this speed.
Q#18
Two satellites going in the equatorial plane have almost same radii. As seen from the earth one move from east to west and the other from west to east. Will they have the same time period as seen from the earth? If not, which one will have less time period?
Answer:
As seen from the earth, the apparent time period for both the satellite will be different due to the rotation of the earth. The earth rotates from west o east. So, the satellite moving from east to west will have greater relative angular speed, hence, will have less time period.
Q#19
A spacecraft consumes more fuel in going from the earth to the moon than it takes for a return trip. Comment on the statement.
Answer:
It is true because in the first case the spacecraft has to spend more fuel to escape from the gravitational field of the earth (which is more than the moon) and to enter moon's field. In the second case, the fuel spent on escaping the moon's gravitation is less because it is up to the lesser distance.
Q#16
No part of India is situated on the equator? Is it possible to have a geostationary satellite which always remains over New Delhi?
Answer: No.
Q#17
As the earth rotates about its axis, a person living in his house at the equator goes in a circular orbit of radius equal to the radius of the earth. Why does he/she not feel weightless as a satellite passenger does?
Answer:
To feel the weightlessness in a circular orbit around the earth, the person should orbit with such a speed so that the centrifugal force must be equal to the apparent weight of the person. For this condition g = v²/R at earth's surface. This gives,
v =√gR = √(9.8 x 6400000) = 7920 m/s = 7.92 km/s
So only going in the circular orbit at the surface of the earth is not sufficient for the weightlessness but his speed also should be 7.92 km/s which is not possible for a person even in a vehicle or plane. Also, the resistance of air on the surface will make the vehicle burn at this speed.
Q#18
Two satellites going in the equatorial plane have almost same radii. As seen from the earth one move from east to west and the other from west to east. Will they have the same time period as seen from the earth? If not, which one will have less time period?
Answer:
As seen from the earth, the apparent time period for both the satellite will be different due to the rotation of the earth. The earth rotates from west o east. So, the satellite moving from east to west will have greater relative angular speed, hence, will have less time period.
Q#19
A spacecraft consumes more fuel in going from the earth to the moon than it takes for a return trip. Comment on the statement.
Answer:
It is true because in the first case the spacecraft has to spend more fuel to escape from the gravitational field of the earth (which is more than the moon) and to enter moon's field. In the second case, the fuel spent on escaping the moon's gravitation is less because it is up to the lesser distance.
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