Myself Abid Ali Fakir,from Marchwari-03, Rupandehi. I worked as a science teacher at Marchawar Rise School.
This is our Force and Motion volume 2 blog and this blog contain all 'Give reason' from Asmita book publication. Numerical based questions is on vol-3,so follow us.
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Difference between
1. Gravitational constant'G' and Acceleration due to gravity 'g'
Ans: Download pdf
2. Gravity and gravitation
3. Weight and mass
4. Free fall and weightlessness
Give reasons
5. Weight varies with location, while the mass remains constant.
Ans: It is because weight directly proportional to acceleration due to gravity 'g' but mass doesn't depends on anything due to which the value of weight also different.
6. The value of acceleration due to gravity is greater on Jupiter than on Earth.
Ans: The value of acceleration due to gravity is greater on Jupiter than the on Earth because mass of Jupiter is 319 times more than the Earth's . And ,we know 'g' directly proportional to mass of object.
7. The acceleration due to gravity near the surface of the moon is smaller than on Earth.
Ans: . The acceleration due to gravity near the surface of the moon is smaller than on earth because of less mass (m) and less radius (R) of the moon than the earth.
8. As you climb Mount Everest, the weight of the goods that you carry decreases.
Ans: Because of acceleration due to gravity 'g', as we climb Mount Everest the height increased and 'g' inversely proportional to acceleration due to gravity.
9. Jumping from a significant height may cause more injury.
Ans: Jumping from a significant height can cause more injury because the impact with the ground is harder, which puts more stress on your body and can lead to serious injuries.
10. The mass of Jupiter is about 319 times the mass of the earth,but it's acceleration due to gravity of the earth.
Ans: Because radius of Jupiter is only 11 times more than earth.And we know that acceleration due to gravity inversely proportional to radius (R).
11. It is difficult to lift a big stone on the surface of the earth,but it is easy to lift a smaller one.
Ans: Because weight of big stone is more and small has less weight and the force required to lift object is directly proportional to mass.
12. Out of two paper sheets, one is folded to form a ball. If the paper ball and the sheet of paper are dropped simultaneously in the air ,the folded paper will fall faster .
Ans: Paper ball reached faster due to less surface area which experienced less air resistance and papersheet reached slightly slow due to more surface which experienced more air resistance.
13. An object thrown horizontally and an object dropped vertically will both hit the ground at the same time.
Ans: Acceleration due to gravity 'g' acts same on both objects due to which both will reach at same time.
14. When a marbel and a feather are dropped simultaneously in a vacuum,they reach the ground together.
Ans: When a marbel and a feather are dropped simultaneously in a vacuum,they reach the ground together because of no air resistance and acceleration due to gravity acts equally on both objects.
15. One will have an eerie feeling when he/she moves down while playing a rote ping.
Ans: One will have an eerie feeling when he/she moves down while playing a rote ping due to sudden change in acceleration due to gravity which make feel us like drooping.
16. Among the objects dropped from the same height in the polar region and the equatorial region of the earth,the object dropped in the polar region falls faster.
Ans: The object dropped in the polar region falls faster because of more acceleration due to gravity which makes them to fall faster.
Long Questions
1. Acceleration due to gravity of there heavenly bodies are given in the table alongside. In the basis of it write the answer of the following questions.
I. Ans: It is easier to lift object in 'C' heavenly body. Because 'C' has less acceleration due to gravity (1.67 m/s^2) which means weight of object in C is less than other.
ii. Ans: If an object dropped from the same height in all there heavenly bodies then object will fall faster in heavenly body 'A' because A has more acceleration due to gravity (g) which means it attract faster towards it's center than other heavenly bodies.
2. The gravitational force between two masses when they are separated by certain distance are shown in the given table.
I. Ans: With reference of serail 1, serail 4 is true.
ii. When we doubled distance between two masses then Gravitational force become 1/4.
Then,
Let, New force after doubled distance be F2
F2=1/4F
= 1/4 x 400 (given)
= 400/400
= 100 N
3. Khaptad lies at a higher altitude than Dhangadhi from the sea level. In these two places,where will be more weight of an object? Give a reason and explain the relation.
Ans: Dhangadhi has more weight because Dhangadhi lies at low altitude due to low altitude it's 'g' become more (g inversely proportional to R+h). And we know that weight 'W' directly proportional to acceleration due to gravity due to more 'g' weight measured in Dhangadhi will be more than Khaptad.
4. Prove that : g = GM/R^2
Solution,
Let a heavenly bodies whose mass is (M) and Radius be (R) attract smaller bodies whose mass is (m) .
Now, form Newton's Universal law of gravitation
F = GM x m/R^2 .................. eq.(1)
Now form Newton's second law of motion
F = m x g .............. eq (2)
Now substitute eq (1) and eq(2)
F = GM x m/R^2
m x g = GM x m / R^2
Cancel m from both sides.
g = GM /R^2
Proved.
5. Prove that: g' = g x ( R/ R+h)
Assumptions:
g is the acceleration due to gravity at the Earth's surface.
g' is the acceleration due to gravity at a height h above the Earth's surface.
R is the radius of the Earth.
We assume the Earth is a perfect sphere with uniform mass distribution.
Derivation:
Gravitational Force:
F = G * (M * m) / r^2, where:
F is the gravitational force
G is the gravitational constant
M is the mass of the Earth
m is the mass of the object
r is the distance between the centers of the Earth and the object
Acceleration due to gravity:
g = F / m = G * M / r^2
At height h:
The distance between the centers of the Earth and the object becomes (R + h).
So, g' = G * M / (R + h)^2
Ratio of g' to g:
g' / g = (G * M / (R + h)^2) / (G * M / R^2)
Simplifying, we get:
g' / g = (R / (R + h))^2
Therefore, g' = g * (R / (R + h))^2
Proof 6:
Equation: g' = g * (R - x) / R
Assumptions:
g is the acceleration due to gravity at the Earth's surface.
g' is the acceleration due to gravity at a depth x below the Earth's surface.
R is the radius of the Earth.
We assume the Earth is a perfect sphere with uniform mass distribution.
Derivation:
Gravitational Force:
As in proof 5, F = G * (M * m) / r^2
Acceleration due to gravity:
g = F / m = G * M / R^2
At depth x:
Only the mass of the Earth within a sphere of radius (R - x) contributes to the gravitational force.
The mass of this sphere is proportional to (R - x)^3.
So, g' = G * (M * (R - x)^3 / R^3) / (R - x)^2
Simplifying, we get:
g' = G * M * (R - x) / R^3
Ratio of g' to g:
g' / g = (G * M * (R - x) / R^3) / (G * M / R^2)
Simplifying, we get:
g' / g = (R - x) / R
Therefore, g' = g * (R - x) / R
Note: These proofs are based on simplified assumptions. In reality, the Earth is not a perfect sphere with uniform mass distribution, and the variation of gravitational acceleration with height and depth is more complex. However, these equations provide a good approximation for relatively small values of h and x compared to the Earth's radius
First blog on force and Motion
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