JEE Exam > JEE 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, respectively 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 just before collision is
- a)2.5 R
- b)4.5 R
- c)7.5 R
- d)1.5 R
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Two spherical bodies of mass M and 5 M and radii R and 2 R, respective...
Let at O, a collision. If small sphere moves x distance and Big sphere moves (9R - c) distance.
Divide eq (1) by eq (2)
Most Upvoted Answer
Two spherical bodies of mass M and 5 M and radii R and 2 R, respective...
U said that the distance of small sphere is x then how that bigger sphere distance became a 9R-x
Free Test
FREE
| Start Free Test |
Community Answer
Two spherical bodies of mass M and 5 M and radii R and 2 R, respective...
Initial Conditions
Given:
- Mass of smaller body (m1) = M
- Mass of larger body (m2) = 5M
- Radius of smaller body (r1) = R
- Radius of larger body (r2) = 2R
- Initial separation between their centers (d) = 12R
Gravitational Force between the Bodies
The gravitational force between two bodies is given by the equation:
F = G * ((m1 * m2) / d^2)
where:
- F is the gravitational force between the bodies
- G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
- m1 and m2 are the masses of the bodies
- d is the separation between their centers
Acceleration of the Smaller Body
The acceleration (a) of the smaller body can be calculated using Newton's second law of motion:
F = m1 * a
Substituting the value of F from the previous equation, we get:
G * ((m1 * m2) / d^2) = m1 * a
Simplifying the equation, we find:
a = (G * m2) / d^2
Time taken for Collision
To find the time taken (t) for the smaller body to collide with the larger body, we can use the equation of motion:
d = ut + (1/2) * a * t^2
where:
- u is the initial velocity of the smaller body (which is 0 in this case)
- a is the acceleration of the smaller body calculated previously
- t is the time taken for the collision
Simplifying the equation, we get:
t^2 = (2 * d) / a
t = √((2 * d) / a)
Distance covered by the Smaller Body
The distance covered by the smaller body just before the collision can be calculated using the equation of motion:
s = ut + (1/2) * a * t^2
where:
- s is the distance covered by the smaller body
- u is the initial velocity of the smaller body (which is 0 in this case)
- a is the acceleration of the smaller body calculated previously
- t is the time taken for the collision
Substituting the value of t, we get:
s = (1/2) * a * (√((2 * d) / a))^2
Simplifying the equation, we find:
s = (1/2) * a * ((2 * d) / a)
s = d
Therefore, the distance covered by the smaller body just before the collision is equal to the initial separation between their centers, which is 12R.
Answer:
The correct option is (c) 7.5R.
Given:
- Mass of smaller body (m1) = M
- Mass of larger body (m2) = 5M
- Radius of smaller body (r1) = R
- Radius of larger body (r2) = 2R
- Initial separation between their centers (d) = 12R
Gravitational Force between the Bodies
The gravitational force between two bodies is given by the equation:
F = G * ((m1 * m2) / d^2)
where:
- F is the gravitational force between the bodies
- G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
- m1 and m2 are the masses of the bodies
- d is the separation between their centers
Acceleration of the Smaller Body
The acceleration (a) of the smaller body can be calculated using Newton's second law of motion:
F = m1 * a
Substituting the value of F from the previous equation, we get:
G * ((m1 * m2) / d^2) = m1 * a
Simplifying the equation, we find:
a = (G * m2) / d^2
Time taken for Collision
To find the time taken (t) for the smaller body to collide with the larger body, we can use the equation of motion:
d = ut + (1/2) * a * t^2
where:
- u is the initial velocity of the smaller body (which is 0 in this case)
- a is the acceleration of the smaller body calculated previously
- t is the time taken for the collision
Simplifying the equation, we get:
t^2 = (2 * d) / a
t = √((2 * d) / a)
Distance covered by the Smaller Body
The distance covered by the smaller body just before the collision can be calculated using the equation of motion:
s = ut + (1/2) * a * t^2
where:
- s is the distance covered by the smaller body
- u is the initial velocity of the smaller body (which is 0 in this case)
- a is the acceleration of the smaller body calculated previously
- t is the time taken for the collision
Substituting the value of t, we get:
s = (1/2) * a * (√((2 * d) / a))^2
Simplifying the equation, we find:
s = (1/2) * a * ((2 * d) / a)
s = d
Therefore, the distance covered by the smaller body just before the collision is equal to the initial separation between their centers, which is 12R.
Answer:
The correct option is (c) 7.5R.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Two spherical bodies of mass M and 5 M and radii R and 2 R, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. Can you explain this answer?
Question Description
Two spherical bodies of mass M and 5 M and radii R and 2 R, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two spherical bodies of mass M and 5 M and radii R and 2 R, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 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, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. Can you explain this answer?.
Two spherical bodies of mass M and 5 M and radii R and 2 R, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two spherical bodies of mass M and 5 M and radii R and 2 R, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 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, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Two spherical bodies of mass M and 5 M and radii R and 2 R, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE 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, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. 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, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two spherical bodies of mass M and 5 M and radii R and 2 R, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. 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, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. 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, respectively 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 just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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