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The acceleration due to gravity (g) on the surface of the earth is approximately 2.6 times that on the surface of the Mars. Given that the radius of the Mars is about one half the radius of the Earth, the ratio of the escape velocity on the Mars to that on the Earth is approximately?
  • a)
    0.44
  • b)
    0.46
  • c)
    0.50
  • d)
    0.47
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The acceleration due to gravity (g) on the surface of the earth is app...
To find the ratio of the escape velocity on Mars to that on Earth, we need to understand the concept of escape velocity and its relation to the acceleration due to gravity.

1. Understanding Escape Velocity:
Escape velocity is the minimum velocity an object must have to escape the gravitational pull of a planet or celestial body. It is the speed required to overcome the gravitational force and allow an object to move away indefinitely.

2. Relation between Escape Velocity and Acceleration due to Gravity:
The escape velocity (V) can be calculated using the formula: V = √(2gR), where g is the acceleration due to gravity and R is the radius of the celestial body.

3. Given Information:
- The acceleration due to gravity on Earth (g₁) is approximately 2.6 times that on Mars (g₂).
- The radius of Mars (R₂) is about one half the radius of Earth (R₁).

4. Calculation:
Let's assume the escape velocity on Earth is V₁ and on Mars is V₂.

From the formula for escape velocity, we can write:
V₁ = √(2g₁R₁)
V₂ = √(2g₂R₂)

Now, substituting the given information:
V₁ = √(2g₁R₁)
V₂ = √(2g₂R₂)
g₁ = 2.6g₂
R₂ = 0.5R₁

Substituting these values into the equations:
V₁ = √(2(2.6g₂)R₁)
V₂ = √(2g₂(0.5R₁))

Simplifying further:
V₁ = √(5.2g₂R₁)
V₂ = √(g₂R₁)

Taking the ratio of V₂ to V₁:
(V₂/V₁) = (√(g₂R₁)/√(5.2g₂R₁))
= (√(g₂R₁)/(√(5.2)√(g₂R₁)))
= (√(g₂R₁)/(√(5.2)√(g₂)√(R₁)))
= (1/√(5.2))

Approximately:
(V₂/V₁) ≈ 0.447

Therefore, the ratio of the escape velocity on Mars to that on Earth is approximately 0.44.

Hence, the correct answer is option 'A' (0.44).
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Community Answer
The acceleration due to gravity (g) on the surface of the earth is app...
We are given that the ge= 2.6 gm and 2rm= re.
where ge is the gravity due to earth and gm is the gravity due to Mars.
also, re and rm be the radius of the earth and Mars respectively.
Now as we are asked about the escape velocity so escape velocity is given by;
We have to take the ratio of Mars to that of earth we get:
Putting all the given value we get the ratio to be = 
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The acceleration due to gravity (g) on the surface of the earth is approximately 2.6 times that on the surface of the Mars. Given that the radius of the Mars is about one half the radius of the Earth, the ratio of the escape velocity on the Mars to that on the Earth is approximately?a)0.44b)0.46c)0.50d)0.47Correct answer is option 'A'. Can you explain this answer?
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The acceleration due to gravity (g) on the surface of the earth is approximately 2.6 times that on the surface of the Mars. Given that the radius of the Mars is about one half the radius of the Earth, the ratio of the escape velocity on the Mars to that on the Earth is approximately?a)0.44b)0.46c)0.50d)0.47Correct answer is option 'A'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about The acceleration due to gravity (g) on the surface of the earth is approximately 2.6 times that on the surface of the Mars. Given that the radius of the Mars is about one half the radius of the Earth, the ratio of the escape velocity on the Mars to that on the Earth is approximately?a)0.44b)0.46c)0.50d)0.47Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The acceleration due to gravity (g) on the surface of the earth is approximately 2.6 times that on the surface of the Mars. Given that the radius of the Mars is about one half the radius of the Earth, the ratio of the escape velocity on the Mars to that on the Earth is approximately?a)0.44b)0.46c)0.50d)0.47Correct answer is option 'A'. Can you explain this answer?.
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