NEET Exam > NEET Questions > An object is projected vertically upwards wit...
Start Learning for Free
An object is projected vertically upwards with a velocity (gr) 1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?
- a)R/2
- b)R
- c)2R
- d)4R
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
An object is projected vertically upwards with a velocity (gr)1/2. Wha...
From the law of conservation of energy, we have;
(m x v2)/2 – (G x M x m)/R = -(G x M x m)/(R+h)
m = Mass of object
M = Mass of earth
h = Maximum height of the object
v = Velocity of projection
(m x v2)/2 – (g x m x R) = -(g x m x R2)/(R+h)
(g x R)/2 = (g x R x h)/(R+h)
Therefore; h = R.
(m x v2)/2 – (G x M x m)/R = -(G x M x m)/(R+h)
m = Mass of object
M = Mass of earth
h = Maximum height of the object
v = Velocity of projection
(m x v2)/2 – (g x m x R) = -(g x m x R2)/(R+h)
(g x R)/2 = (g x R x h)/(R+h)
Therefore; h = R.
Free Test
FREE
| Start Free Test |
Community Answer
An object is projected vertically upwards with a velocity (gr)1/2. Wha...
Understanding the Problem
When an object is projected vertically upwards with an initial velocity of (gr)^(1/2), we need to determine the maximum height it reaches in relation to the Earth's radius, R.
Key Concepts
- Initial Velocity (u): (gr)^(1/2)
- Acceleration due to Gravity (g): Decreases with height.
Maximum Height Calculation
1. Using Kinematic Equation: The maximum height (h) can be found using the equation of motion:
- v^2 = u^2 - 2gh
- At maximum height, the final velocity (v) is 0.
2. Substituting Values:
- 0 = (gr) + 2g(h)
- Rearranging gives: 2gh = gr
- Thus, h = r/2
Considering Gravity Variation
- Gravity decreases with height according to the formula:
- g' = g(1 - h/R)
- At maximum height, we need to consider the varying gravitational force.
Setting Up the Equation
1. Replace g with the new value:
- g' = g(1 - h/R)
2. Final Equation:
- The object will stop when the kinetic energy converts into potential energy.
- This results in the height being approximately equal to R under normal conditions.
Conclusion
Considering the maximum height reached and the fact that g decreases as the object goes higher, the maximum height achieved is effectively equal to R.
Therefore, the maximum height reached by the object is:
Final Answer: R
When an object is projected vertically upwards with an initial velocity of (gr)^(1/2), we need to determine the maximum height it reaches in relation to the Earth's radius, R.
Key Concepts
- Initial Velocity (u): (gr)^(1/2)
- Acceleration due to Gravity (g): Decreases with height.
Maximum Height Calculation
1. Using Kinematic Equation: The maximum height (h) can be found using the equation of motion:
- v^2 = u^2 - 2gh
- At maximum height, the final velocity (v) is 0.
2. Substituting Values:
- 0 = (gr) + 2g(h)
- Rearranging gives: 2gh = gr
- Thus, h = r/2
Considering Gravity Variation
- Gravity decreases with height according to the formula:
- g' = g(1 - h/R)
- At maximum height, we need to consider the varying gravitational force.
Setting Up the Equation
1. Replace g with the new value:
- g' = g(1 - h/R)
2. Final Equation:
- The object will stop when the kinetic energy converts into potential energy.
- This results in the height being approximately equal to R under normal conditions.
Conclusion
Considering the maximum height reached and the fact that g decreases as the object goes higher, the maximum height achieved is effectively equal to R.
Therefore, the maximum height reached by the object is:
Final Answer: R
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect answer is option 'B'. Can you explain this answer?
Question Description
An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect 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 An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect 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 An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect answer is option 'B'. Can you explain this answer?.
An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect 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 An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect 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 An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect answer is option 'B'. Can you explain this answer?.
Solutions for An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An object is projected vertically upwards with a velocity (gr)1/2. What is the maximum height reached by the object if “R” is the radius of the earth and “g” is the acceleration due to gravity?a)R/2b)Rc)2Rd)4RCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup