“Conceptual Questions”
Q 1. If there is an attractive force between all objects why don’t we feel ourselves graviting towards near by Massive buildings?
Answer:
We do not feel ourselves graviting towards nearby messive buildings because of the following two reasons.
First reason:
The gravitational force between two bodies is an example of Newton’s third law of motion. Both bodies exert force of same magnitude and opposite direction on each other. Therefore we do not feel ourselves graviting towards nearby massive buildings.
F12=-F21
Second Reason:
The magnitude of this force is extremely small to detect that is why we do not feel ourselves graviting towards nearby massive buildings.
e.g If mass of a person is 100kg and that of building is 10,000 kg . Distance between both is 1m. Then force of attraction is
F=Gm1m2/r² ……. (i)
F= 6.67×10-11Nm²kg-2× 100 kg × 10,000 kg / (1m)²
F= 6.7× 10-6N
As this is extremely small to detect . So we can not detect this force.
Q 2. Does the sun exert a larger force on Earth then that exerted on the sun by the earth. Explain.
Answer:
Both earth and sun will exert same force on each other.
Explanation:
According to Newton’s law of universal gravitation, both earth and sun will exert force on each other. This force is given by,
F= GMeMs/r²
According to this law these two forces will be equal in magnitude but opposite in direction following Newton’s third law of motion.
F12=-F21
That is why both sun and earth will exert same force on each other.
Q 3. What is importance of gravitational constant “G”? Why is it difficult to calculate?
Answer:
G is known as Gravitational constant and it’s value is 6.67×10-11Nm²/kg². This value is independent of size of bodies, and nature of medium or anything. It’s value remains same throughout the Universe.
Importance :
The gravitational constant plays an important role in the universe. We can find Mass , radius , gravity of any astronomical object with the help of this Gravitational constant G.
Why its value of difficult to calculate?
The value of G is difficult to determine because
i) We measure it with gravity and gravity is a weaker force than any other fundamental force.
ii) No instrument apparatus can separate from gravitational influence of other bodies.
iii) Gravity has no established relation to other fundamental forces.
Q4. If earth somehow expanded to a larger radius , with no change in mass , how would your weight be affected? How would it be affected if earth instead shrunk?
Answer:
a) If earth is expanded to larger radius with no change in mass , weight will decrease.
b) If the earth shrinks, with no change in mass then our weight will increase.
Explanation:
We know that ,
g = GMe/Re²
As we know that , w= mg
g = w/m
w/m = GMe /Re²
w = mGMe/Re² …….. (i)
Above equation shows that weight is inversely proportional to radius of Earth if mass of Earth is constant. So,
a) if earth somehow extended to larger radius, without any change in mass the weight of body will decrease.
b) if Earth instead shrunk to smaller radius without any change in mass , weight of body will increase
Q5. What would happen to your weight on Earth if mass of Earth is doubled but its radius remains same?
Answer:
Our weight will be doubled if mass of Earth is doubled but it’s radius remains same.
We know that ,
g = GMe/Re²
As we know that , w= mg
g = w/m
w/m = GMe /Re²
w = mGMe/Re² …….. (i)
Above equation shows that weight of object is directly proportional to mass of Earth if radius remains same. Now if mass of Earth is doubled,
Me’ = 2Me
w’ = mGMe’/Re²
w’ = mG2Me/Re²
w’ = 2 (mGMe/Re²)
w’= 2w
It means our weight will be doubled if mass of Earth is doubled but its radius remains same.
Q6. Why lighter and heavier objects fall towards Earth at the same rate?
Answer :
The lighter and heavier objects fall towards Earth at the same rate because a acceleration due to gravity does not depend on mass of body.
Explanation:
We know that aceleration due to gravity is given by,
g = GMe/Re² ……(i)
Above equation shows that the acceleration due to gravity depends upon mass of earth and radius of earth. It does not depend on mass of object. So lighter and heavier objects will fall towards Earth at the same rate.
Q7. The value of g changes with location on earth, however we take the same value of g everywhere on earth 9.8m/s² for ordinary calculations? Why?
Answer:
We take the value of g = 9.8m/s² everywhere on earth because there is very slight change in the value of g.
Explanation:
We know that the value of g is given by
g = GMe/Re² ……(i)
Equation shows that the value of g depends upon radius of earth. As the radius of earth at equator and poles is different so value of g is different at equator and poles. But difference between radius of equator and poles is very less so change in value of very small . Due to this reason we take the value of g on average 9.8m/s².
Q8. Moon is attracted by earth why it does not fall on earth?
Answer :
Moon does not fall on Earth due to action reaction forces.
Explanation:
According to law of universal gravitation, there is a force of attraction between moon and earth which is given by,
Fg = GMeMm/r² ……..(i)
The gravitational force of Earth on moon provides centripetal force to the moon. According to law of universal gravitation moon also exerts force of same magnitude but opposite direction on earth. This force of moon is acting away from earth which provides centrifugal force to the moon. This centripetal force and centrifugal force follow Newton’s third law of motion and balance each other. That is why moon does not fall on earth.
Q9. Why for same height smaller and larger satellite must have same orbital speed?
Answer :
For same height smaller and largest satellite must have same orbital speed because speed of satellite does not depend upon mass of satellite.
Explanation:
We know that speed of satellite around Earth is given by,
v = √GMe/(Re+h) ……(i)
Above equation shows that speed of satellite depends upon mass of earth and its height from the center of earth.
It does not depend on mass of satellite. So for same height, smaller and larger satellites must have same orbital speed .
