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A planet has mass 1/10 of that of earth, while radius is 1/3 that of earth. If a person can throw a stone on earth surface to a height of 90m, then he will be able to throw the stone on that planet to a height
- a)90m
- b)40m
- c)100m
- d)45m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A planet has mass 1/10 of that of earth, while radius is 1/3 that of e...
Let mass of earth be M
Acceleration due to gravity = g
Radius of earth = r
Height to which he can throw on earth = H
Acceleration due to gravity at the planet be = g'
Radius of the planet be= r'
Mass of the planet be = M'
Height to which he can throw at that planet = H'
Then g = G(M/r^2)
Therefore g' = G{(1/10)M}/[{(1/3)r}^2]
= (9/10) G(M/r^2)
= (9/10)g
Now, H = {(v)^2-(u)^2}/2(-g)
= {(0)^2-(u)^2}/(-2g)
= {(u)^2}/2g
H' = u^2/[2{(9/10)g}]
= (10/9)u^2/2g
= (10/9)H
= (10/9) * 90
= 100 m
Acceleration due to gravity = g
Radius of earth = r
Height to which he can throw on earth = H
Acceleration due to gravity at the planet be = g'
Radius of the planet be= r'
Mass of the planet be = M'
Height to which he can throw at that planet = H'
Then g = G(M/r^2)
Therefore g' = G{(1/10)M}/[{(1/3)r}^2]
= (9/10) G(M/r^2)
= (9/10)g
Now, H = {(v)^2-(u)^2}/2(-g)
= {(0)^2-(u)^2}/(-2g)
= {(u)^2}/2g
H' = u^2/[2{(9/10)g}]
= (10/9)u^2/2g
= (10/9)H
= (10/9) * 90
= 100 m
Most Upvoted Answer
A planet has mass 1/10 of that of earth, while radius is 1/3 that of e...
Let mass of earth be M
accelaration due to gravity =g
radius of earth be= r
heaight to which he can throw on earth = H
accelaration due to gravity at the planet be =g'
radius of the planet be= r'
mass of the planet be= M'
height to which he can throw at that planet be= H'
then g=G(M/r^2)
therefore g'= G{(1/10)M}/[{(1/3)r}^2]
=(9/10) G(M/r^2)
=(9/10)g
now H={( v)^2-(u)^2}/2(-g)
={(0)^2-(u)^2}/(-2g)
= {(u)^2}/2g
H'= u^2/[2{(9/10)g}]
=(10/9)u^2/2g
=(10/9)H
=(10/9) * 90
=100
accelaration due to gravity =g
radius of earth be= r
heaight to which he can throw on earth = H
accelaration due to gravity at the planet be =g'
radius of the planet be= r'
mass of the planet be= M'
height to which he can throw at that planet be= H'
then g=G(M/r^2)
therefore g'= G{(1/10)M}/[{(1/3)r}^2]
=(9/10) G(M/r^2)
=(9/10)g
now H={( v)^2-(u)^2}/2(-g)
={(0)^2-(u)^2}/(-2g)
= {(u)^2}/2g
H'= u^2/[2{(9/10)g}]
=(10/9)u^2/2g
=(10/9)H
=(10/9) * 90
=100
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Community Answer
A planet has mass 1/10 of that of earth, while radius is 1/3 that of e...
Given:
Mass of the planet = 1/10 of the mass of Earth
Radius of the planet = 1/3 of the radius of Earth
Height to which a stone can be thrown on Earth = 90m
To determine the height to which the stone can be thrown on the planet, we need to compare the gravitational forces on the two objects.
1. Gravitational Force:
The gravitational force between two objects is given by the equation:
F = G * (m1 * m2) / r^2
2. Comparison of Gravitational Forces:
Since the mass of the planet is 1/10 of the mass of Earth, the gravitational force on the planet will be 1/10 of the gravitational force on Earth. This is because the force is directly proportional to the mass.
3. Comparison of Radii:
The radius of the planet is 1/3 of the radius of Earth. The gravitational force is inversely proportional to the square of the radius. Therefore, the gravitational force on the planet will be (1/3)^2 = 1/9 of the gravitational force on Earth.
4. Comparison of Heights:
Since the gravitational force on the planet is 1/10 of the gravitational force on Earth and the radius of the planet is 1/3 of the radius of Earth, the height to which the stone can be thrown on the planet will be:
Height on planet = (1/10) * (1/9) * 90m
= 1/90 * 90m
= 1m
Therefore, the stone can be thrown to a height of 1m on the planet.
The correct answer is option C) 100m.
Mass of the planet = 1/10 of the mass of Earth
Radius of the planet = 1/3 of the radius of Earth
Height to which a stone can be thrown on Earth = 90m
To determine the height to which the stone can be thrown on the planet, we need to compare the gravitational forces on the two objects.
1. Gravitational Force:
The gravitational force between two objects is given by the equation:
F = G * (m1 * m2) / r^2
2. Comparison of Gravitational Forces:
Since the mass of the planet is 1/10 of the mass of Earth, the gravitational force on the planet will be 1/10 of the gravitational force on Earth. This is because the force is directly proportional to the mass.
3. Comparison of Radii:
The radius of the planet is 1/3 of the radius of Earth. The gravitational force is inversely proportional to the square of the radius. Therefore, the gravitational force on the planet will be (1/3)^2 = 1/9 of the gravitational force on Earth.
4. Comparison of Heights:
Since the gravitational force on the planet is 1/10 of the gravitational force on Earth and the radius of the planet is 1/3 of the radius of Earth, the height to which the stone can be thrown on the planet will be:
Height on planet = (1/10) * (1/9) * 90m
= 1/90 * 90m
= 1m
Therefore, the stone can be thrown to a height of 1m on the planet.
The correct answer is option C) 100m.
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A planet has mass 1/10 of that of earth, while radius is 1/3 that of earth. If a person can throw a stone on earth surface to a height of 90m, then he will be able to throw the stone on that planet to a heighta)90mb)40mc)100md)45mCorrect answer is option 'C'. Can you explain this answer?
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