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The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :
- a)v
- b)2v
- c)3v
- d)4v
Correct answer is option 'D'. Can you explain this answer?
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The escape velocity from the Earths surface is v. The escape velocity ...
Escape Velocity:
Escape velocity is the minimum velocity required for an object to escape the gravitational pull of a celestial body. It is the speed needed for an object to break free from the gravitational force and move away indefinitely.
Formula for Escape Velocity:
The formula to calculate escape velocity is given by:
v = sqrt((2GM)/r)
Where,
v = escape velocity,
G = gravitational constant,
M = mass of the planet,
r = radius of the planet.
Escape Velocity and Radius Relationship:
The escape velocity is directly proportional to the square root of the mass of the planet and inversely proportional to the square root of the radius of the planet. Mathematically, it can be expressed as:
v ∝ sqrt(M/r)
Given Information:
- Escape velocity from the Earth's surface is v.
- The radius of the other planet is four times that of Earth.
- The mass density of both planets is the same.
Solution:
To find the escape velocity from the surface of the other planet, we need to compare the ratios of the escape velocities.
Step 1: Find the ratio of the escape velocities of Earth and the other planet using the formula:
v1/v2 = sqrt((M1/M2)*(r2/r1))
Here, M1 and M2 are the masses of Earth and the other planet respectively, and r1 and r2 are their respective radii.
Step 2: Substitute the given information:
- M1 = M2 (same mass density)
- r2 = 4r1 (radius of the other planet is four times that of Earth)
Step 3: Simplify and solve the equation:
v1/v2 = sqrt((1/1)*(4r1/r1))
v1/v2 = sqrt(4)
v1/v2 = 2
This implies that the escape velocity from the surface of the other planet is twice the escape velocity from the Earth's surface.
Step 4: Compare the given options:
a) v
b) 2v
c) 3v
d) 4v
Since the ratio of the escape velocities is 2, the correct answer is option 'D' - 4v.
Escape velocity is the minimum velocity required for an object to escape the gravitational pull of a celestial body. It is the speed needed for an object to break free from the gravitational force and move away indefinitely.
Formula for Escape Velocity:
The formula to calculate escape velocity is given by:
v = sqrt((2GM)/r)
Where,
v = escape velocity,
G = gravitational constant,
M = mass of the planet,
r = radius of the planet.
Escape Velocity and Radius Relationship:
The escape velocity is directly proportional to the square root of the mass of the planet and inversely proportional to the square root of the radius of the planet. Mathematically, it can be expressed as:
v ∝ sqrt(M/r)
Given Information:
- Escape velocity from the Earth's surface is v.
- The radius of the other planet is four times that of Earth.
- The mass density of both planets is the same.
Solution:
To find the escape velocity from the surface of the other planet, we need to compare the ratios of the escape velocities.
Step 1: Find the ratio of the escape velocities of Earth and the other planet using the formula:
v1/v2 = sqrt((M1/M2)*(r2/r1))
Here, M1 and M2 are the masses of Earth and the other planet respectively, and r1 and r2 are their respective radii.
Step 2: Substitute the given information:
- M1 = M2 (same mass density)
- r2 = 4r1 (radius of the other planet is four times that of Earth)
Step 3: Simplify and solve the equation:
v1/v2 = sqrt((1/1)*(4r1/r1))
v1/v2 = sqrt(4)
v1/v2 = 2
This implies that the escape velocity from the surface of the other planet is twice the escape velocity from the Earth's surface.
Step 4: Compare the given options:
a) v
b) 2v
c) 3v
d) 4v
Since the ratio of the escape velocities is 2, the correct answer is option 'D' - 4v.
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Community Answer
The escape velocity from the Earths surface is v. The escape velocity ...
As we know escape velocity is given by,
Escape velocity from Earth’s surface = v
Escape velocity from surface of another planet = ?
Rplanet = 4Rearth
Splanet = Searth
So we can write,
It means,
Escape velocity from Earth’s surface = v
Escape velocity from surface of another planet = ?
Rplanet = 4Rearth
Splanet = Searth
So we can write,
It means,
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The escape velocity from the Earths surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :a)vb)2vc)3vd)4vCorrect answer is option 'D'. Can you explain this answer?
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