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The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. VP and VE are escape velocities of the planet and the earth, respectively, then
- a)VP = 1.5VE
- b)VP = 2VE
- c)VE = 3VP
- d)VE = 1.5VP
Correct answer is option 'B'. Can you explain this answer?
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The radius of a planet is twice the radius of earth. Both have almost...
Given information:
- The radius of the planet is twice the radius of Earth.
- Both the planet and Earth have almost equal average mass-densities.
Step 1: Finding the relationship between the radii
Let's assume the radius of Earth is 'R'. According to the given information, the radius of the planet is twice that of Earth, so the radius of the planet will be '2R'.
Step 2: Finding the relationship between the volumes
The volume of a sphere is given by the formula V = (4/3)πr³, where 'V' is the volume and 'r' is the radius.
- The volume of Earth (VE) = (4/3)πR³
- The volume of the planet (VP) = (4/3)π(2R)³ = (4/3)π8R³ = (4/3)π(8R³) = 8(4/3)πR³ = 8VE
Step 3: Finding the relationship between the masses
Since both the planet and Earth have almost equal average mass-densities, their masses will be directly proportional to their volumes. Therefore,
- The mass of Earth (ME) ∝ VE
- The mass of the planet (MP) ∝ VP
Step 4: Finding the relationship between the escape velocities
The escape velocity (v) of an object is given by the formula v = √(2GM/R), where 'G' is the universal gravitational constant, 'M' is the mass of the object, and 'R' is the radius of the object.
- The escape velocity of Earth (VE) = √(2GE*ME/R)
- The escape velocity of the planet (VP) = √(2GP*MP/(2R))
Since the masses of Earth and the planet are proportional to their volumes, we can write:
- ME ∝ VE ∝ R³
- MP ∝ VP ∝ (2R)³ = 8R³
Step 5: Comparing the escape velocities
Comparing the expressions for VE and VP, we can see that:
- VE ∝ R³
- VP ∝ 8R³
Since VP is 8 times the value of VE, we can conclude that VP = 2VE.
Therefore, the correct answer is option 'B': VP = 2VE.
- The radius of the planet is twice the radius of Earth.
- Both the planet and Earth have almost equal average mass-densities.
Step 1: Finding the relationship between the radii
Let's assume the radius of Earth is 'R'. According to the given information, the radius of the planet is twice that of Earth, so the radius of the planet will be '2R'.
Step 2: Finding the relationship between the volumes
The volume of a sphere is given by the formula V = (4/3)πr³, where 'V' is the volume and 'r' is the radius.
- The volume of Earth (VE) = (4/3)πR³
- The volume of the planet (VP) = (4/3)π(2R)³ = (4/3)π8R³ = (4/3)π(8R³) = 8(4/3)πR³ = 8VE
Step 3: Finding the relationship between the masses
Since both the planet and Earth have almost equal average mass-densities, their masses will be directly proportional to their volumes. Therefore,
- The mass of Earth (ME) ∝ VE
- The mass of the planet (MP) ∝ VP
Step 4: Finding the relationship between the escape velocities
The escape velocity (v) of an object is given by the formula v = √(2GM/R), where 'G' is the universal gravitational constant, 'M' is the mass of the object, and 'R' is the radius of the object.
- The escape velocity of Earth (VE) = √(2GE*ME/R)
- The escape velocity of the planet (VP) = √(2GP*MP/(2R))
Since the masses of Earth and the planet are proportional to their volumes, we can write:
- ME ∝ VE ∝ R³
- MP ∝ VP ∝ (2R)³ = 8R³
Step 5: Comparing the escape velocities
Comparing the expressions for VE and VP, we can see that:
- VE ∝ R³
- VP ∝ 8R³
Since VP is 8 times the value of VE, we can conclude that VP = 2VE.
Therefore, the correct answer is option 'B': VP = 2VE.
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Community Answer
The radius of a planet is twice the radius of earth. Both have almost...
Here, Rp = 2RE, ρE=ρP
Escape velocity of the earth, VE
= 
Escape velocity of the planet
Divide (i) by (ii), we get
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The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. VP and VE are escape velocities of the planet and the earth, respectively, thena)VP = 1.5VEb)VP = 2VEc)VE = 3VPd)VE = 1.5VPCorrect answer is option 'B'. Can you explain this answer?
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The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. VP and VE are escape velocities of the planet and the earth, respectively, thena)VP = 1.5VEb)VP = 2VEc)VE = 3VPd)VE = 1.5VPCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. VP and VE are escape velocities of the planet and the earth, respectively, thena)VP = 1.5VEb)VP = 2VEc)VE = 3VPd)VE = 1.5VPCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. VP and VE are escape velocities of the planet and the earth, respectively, thena)VP = 1.5VEb)VP = 2VEc)VE = 3VPd)VE = 1.5VPCorrect answer is option 'B'. Can you explain this answer?.
The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. VP and VE are escape velocities of the planet and the earth, respectively, thena)VP = 1.5VEb)VP = 2VEc)VE = 3VPd)VE = 1.5VPCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. VP and VE are escape velocities of the planet and the earth, respectively, thena)VP = 1.5VEb)VP = 2VEc)VE = 3VPd)VE = 1.5VPCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. VP and VE are escape velocities of the planet and the earth, respectively, thena)VP = 1.5VEb)VP = 2VEc)VE = 3VPd)VE = 1.5VPCorrect answer is option 'B'. Can you explain this answer?.
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