NEET Exam > NEET Questions > Two spherical bodies of mass M and 5 M and ra...
Start Learning for Free
Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initial
separation between their centres equal to 12 R. If they attract each other due to gravitational force
only, then the distance covered by the smaller body before collision is :
separation between their centres equal to 12 R. If they attract each other due to gravitational force
only, then the distance covered by the smaller body before collision is :
- a)1.5 R
- b)2.5 R
- c)4.5 R
- d)7.5 R
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Two spherical bodies of mass M and 5 M and radii R and 2 R are release...
Given:
Mass of smaller body, m = M
Mass of larger body, M = 5M
Radius of smaller body, r = R
Radius of larger body, R = 2R
Initial separation, d = 12R
To find: Distance covered by the smaller body before collision
Concepts used:
1. Gravitational force between two bodies of masses m1 and m2 separated by a distance d is given by:
F = G * m1 * m2 / d^2
where G is the universal gravitational constant
2. Law of conservation of energy:
Total mechanical energy (kinetic energy + potential energy) of a system is conserved in the absence of external forces.
Approach:
1. Find the gravitational force acting between the two bodies at a separation of d.
2. Calculate the initial potential energy of the system.
3. Calculate the velocity of the smaller body at the time of collision using conservation of energy.
4. Use the velocity and acceleration due to gravity to find the time taken by the smaller body to cover the distance d/2 (half the initial separation).
5. Use the time taken to find the distance covered by the smaller body before collision.
Calculation:
1. Gravitational force between the two bodies at a separation of d:
F = G * m1 * m2 / d^2
where m1 = M, m2 = 5M, d = 12R
F = G * M * 5M / (12R)^2
F = G * 5M^2 / (144R^2)
F = 5G * M^2 / (144R^2)
2. Initial potential energy of the system:
U = -G * m1 * m2 / d
where m1 = M, m2 = 5M, d = 12R
U = -G * M * 5M / (12R)
U = -5G * M^2 / (12R)
3. Using conservation of energy:
Initial total mechanical energy = Final total mechanical energy
Initial total mechanical energy = U
Final total mechanical energy = (1/2) * m * v^2 + (1/2) * M * V^2
where v is the velocity of the smaller body at the time of collision
V is the velocity of the larger body at the time of collision (which can be assumed to be zero as it is much larger and takes negligible time to come to rest)
U = (1/2) * m * v^2 + (1/2) * M * V^2
Substituting the values:
-5G * M^2 / (12R) = (1/2) * m * v^2
-5G * M^2 / (12R) = (1/2) * M * v^2
(As m = M)
v^2 = -10G * M / (24R)
v^2 = -G * M / (12R)
4. Time taken by the smaller body to cover the distance d/2:
The acceleration due to gravity acting on the smaller body is:
a = F / m
where F is the gravitational force
Mass of smaller body, m = M
Mass of larger body, M = 5M
Radius of smaller body, r = R
Radius of larger body, R = 2R
Initial separation, d = 12R
To find: Distance covered by the smaller body before collision
Concepts used:
1. Gravitational force between two bodies of masses m1 and m2 separated by a distance d is given by:
F = G * m1 * m2 / d^2
where G is the universal gravitational constant
2. Law of conservation of energy:
Total mechanical energy (kinetic energy + potential energy) of a system is conserved in the absence of external forces.
Approach:
1. Find the gravitational force acting between the two bodies at a separation of d.
2. Calculate the initial potential energy of the system.
3. Calculate the velocity of the smaller body at the time of collision using conservation of energy.
4. Use the velocity and acceleration due to gravity to find the time taken by the smaller body to cover the distance d/2 (half the initial separation).
5. Use the time taken to find the distance covered by the smaller body before collision.
Calculation:
1. Gravitational force between the two bodies at a separation of d:
F = G * m1 * m2 / d^2
where m1 = M, m2 = 5M, d = 12R
F = G * M * 5M / (12R)^2
F = G * 5M^2 / (144R^2)
F = 5G * M^2 / (144R^2)
2. Initial potential energy of the system:
U = -G * m1 * m2 / d
where m1 = M, m2 = 5M, d = 12R
U = -G * M * 5M / (12R)
U = -5G * M^2 / (12R)
3. Using conservation of energy:
Initial total mechanical energy = Final total mechanical energy
Initial total mechanical energy = U
Final total mechanical energy = (1/2) * m * v^2 + (1/2) * M * V^2
where v is the velocity of the smaller body at the time of collision
V is the velocity of the larger body at the time of collision (which can be assumed to be zero as it is much larger and takes negligible time to come to rest)
U = (1/2) * m * v^2 + (1/2) * M * V^2
Substituting the values:
-5G * M^2 / (12R) = (1/2) * m * v^2
-5G * M^2 / (12R) = (1/2) * M * v^2
(As m = M)
v^2 = -10G * M / (24R)
v^2 = -G * M / (12R)
4. Time taken by the smaller body to cover the distance d/2:
The acceleration due to gravity acting on the smaller body is:
a = F / m
where F is the gravitational force
Free Test
FREE
| Start Free Test |
Community Answer
Two spherical bodies of mass M and 5 M and radii R and 2 R are release...
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
Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. Can you explain this answer?
Question Description
Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. 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 Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. Can you explain this answer?.
Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. 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 Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. 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 Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initialseparation between their centres equal to 12 R. If they attract each other due to gravitational forceonly, then the distance covered by the smaller body before collision is :a)1.5 Rb)2.5 Rc)4.5 Rd)7.5 RCorrect answer is option 'D'. 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