Mechanical Engineering Exam  >  Mechanical Engineering Questions  >   Two spherical bodies of mass M and 5M and ra... Start Learning for Free
Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centers equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is-
  • a)
    2.5R
  • b)
    4.5R
  • c)
    1.5R
  • d)
    7.5R
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two spherical bodies of mass M and 5M and radii R and 2R respectively...
Given Data:
Mass of smaller body, m = M
Mass of larger body, M = 5M
Radii of smaller body, r = R
Radii of larger body, R = 2R
Initial separation between their centers = 12R

Approach:
- Calculate the gravitational force between the two bodies
- Use the concept of conservation of mechanical energy to find the distance covered by the smaller body just before collision

Calculations:
1. Gravitational force between the two bodies:
- F = (G * m * M) / (r + 2r)^2
- F = (G * M * 5M) / (3R)^2
- F = (5GM^2) / 9R^2
2. Work done by the gravitational force:
- W = Initial potential energy - Final potential energy
- W = -G * m * M / (r + 2r) + G * m * M / (2r)
- W = -2GM^2 / 3R + GM^2 / 2R
- W = -4GM^2 / 6R + 3GM^2 / 6R
- W = -GM^2 / 6R
3. Using conservation of mechanical energy:
- Initial kinetic energy + Initial potential energy = Final kinetic energy + Final potential energy
- 0 + 0 = 0.5mv^2 + GMm / (r + 2r) - 4GM^2 / 6R
- v = sqrt(2GM / 3R)
4. Distance covered by smaller body before collision:
- d = 1/2 * a * t^2
- d = 1/2 * (GM / (3R)^2) * (2 * 3R / sqrt(2GM / 3R))^2
- d = 7.5R
Therefore, the distance covered by the smaller body just before collision is 7.5R. Hence, the correct answer is option 'D'.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
Explore Courses for Mechanical Engineering exam

Top Courses for Mechanical Engineering

Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centers equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is-a)2.5Rb)4.5Rc)1.5Rd)7.5RCorrect answer is option 'D'. Can you explain this answer?
Question Description
Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centers equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is-a)2.5Rb)4.5Rc)1.5Rd)7.5RCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centers equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is-a)2.5Rb)4.5Rc)1.5Rd)7.5RCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centers equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is-a)2.5Rb)4.5Rc)1.5Rd)7.5RCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centers equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is-a)2.5Rb)4.5Rc)1.5Rd)7.5RCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering. Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centers equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is-a)2.5Rb)4.5Rc)1.5Rd)7.5RCorrect 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 5M and radii R and 2R respectively are released in free space with initial separation between their centers equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is-a)2.5Rb)4.5Rc)1.5Rd)7.5RCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centers equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is-a)2.5Rb)4.5Rc)1.5Rd)7.5RCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centers equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is-a)2.5Rb)4.5Rc)1.5Rd)7.5RCorrect 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 5M and radii R and 2R respectively are released in free space with initial separation between their centers equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is-a)2.5Rb)4.5Rc)1.5Rd)7.5RCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
Explore Courses for Mechanical Engineering exam

Top Courses for Mechanical Engineering

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev