Physics Exam > Physics Questions > A cavity of radiusR/2is made inside a solid s...
Start Learning for Free
A cavity of radius R/2 is made inside a solid sphere of radius R. The centre of the cavity is located at a distance R/2 from centre of the sphere. The gravitational force on a particle of mass m at a distance R/2 from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite to the centre of cavity).
[Here, g = GM/R2, where M is the mass of the sphere without cavity ]
- a)mg/2
- b)3mg/8
- c)mg/16
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A cavity of radiusR/2is made inside a solid sphere of radiusR. The cen...
Gravitational field at mass 'm' due to full solid sphere
Gravitational field at mass 'm' due to cavity (-ρ)
Net gravitational field
Net force on m →
The correct answer is: 3mg/8
Most Upvoted Answer
A cavity of radiusR/2is made inside a solid sphere of radiusR. The cen...
Gravitational field at mass 'm' due to full solid sphere
Gravitational field at mass 'm' due to cavity (-ρ)
Net gravitational field
Net force on m →
The correct answer is: 3mg/8
Free Test
FREE
| Start Free Test |
Community Answer
A cavity of radiusR/2is made inside a solid sphere of radiusR. The cen...
Gravitational force on a particle of mass m at a distance R/2 from the center of the sphere on the line joining both the centers of the sphere and cavity can be found using Newton's law of gravitation.
1. Determine the gravitational force on the particle due to the solid sphere without the cavity.
The mass of the solid sphere is given by M. The distance between the particle and the center of the sphere is R/2. Using Newton's law of gravitation, the gravitational force (F1) on the particle due to the solid sphere is given by:
F1 = (G * M * m) / (R/2)^2
= 4 * (G * M * m) / R^2
2. Determine the gravitational force on the particle due to the cavity.
Since the cavity is a hollow spherical shell, the gravitational force inside the cavity due to the shell is zero. Therefore, the gravitational force on the particle due to the cavity is zero.
3. Determine the total gravitational force on the particle.
The net gravitational force on the particle is the sum of the forces due to the solid sphere and the cavity. Since the force due to the cavity is zero, the total gravitational force (F) on the particle is equal to F1.
F = F1 = 4 * (G * M * m) / R^2
4. Simplify the expression.
Since we are looking for the gravitational force on the particle at a distance R/2 from the center of the sphere, we can substitute R/2 for R in the expression:
F = 4 * (G * M * m) / (R/2)^2
= 4 * (G * M * m) / (R^2/4)
= 16 * (G * M * m) / R^2
5. Simplify further.
Using the given value for g (gravitational acceleration), which is equal to G * M / R^2, we can substitute it into the expression:
F = 16 * (G * M * m) / R^2
= 16 * (g * R^2 * m) / R^2
= 16 * g * m
Therefore, the gravitational force on the particle is 16 times the gravitational force due to the solid sphere without the cavity, which is 16 * mg.
Hence, the correct answer is option B: 3mg/8.
1. Determine the gravitational force on the particle due to the solid sphere without the cavity.
The mass of the solid sphere is given by M. The distance between the particle and the center of the sphere is R/2. Using Newton's law of gravitation, the gravitational force (F1) on the particle due to the solid sphere is given by:
F1 = (G * M * m) / (R/2)^2
= 4 * (G * M * m) / R^2
2. Determine the gravitational force on the particle due to the cavity.
Since the cavity is a hollow spherical shell, the gravitational force inside the cavity due to the shell is zero. Therefore, the gravitational force on the particle due to the cavity is zero.
3. Determine the total gravitational force on the particle.
The net gravitational force on the particle is the sum of the forces due to the solid sphere and the cavity. Since the force due to the cavity is zero, the total gravitational force (F) on the particle is equal to F1.
F = F1 = 4 * (G * M * m) / R^2
4. Simplify the expression.
Since we are looking for the gravitational force on the particle at a distance R/2 from the center of the sphere, we can substitute R/2 for R in the expression:
F = 4 * (G * M * m) / (R/2)^2
= 4 * (G * M * m) / (R^2/4)
= 16 * (G * M * m) / R^2
5. Simplify further.
Using the given value for g (gravitational acceleration), which is equal to G * M / R^2, we can substitute it into the expression:
F = 16 * (G * M * m) / R^2
= 16 * (g * R^2 * m) / R^2
= 16 * g * m
Therefore, the gravitational force on the particle is 16 times the gravitational force due to the solid sphere without the cavity, which is 16 * mg.
Hence, the correct answer is option B: 3mg/8.
|
Explore Courses for Physics exam
|
|
A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer?
Question Description
A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A cavity of radiusR/2is made inside a solid sphere of radiusR. The centre of the cavity is located at a distanceR/2from centre of the sphere. The gravitational force on a particle of massmat a distanceR/2from the centre of the sphere on the line joining both the centres of sphere and cavity is(opposite to the centre of cavity).[Here, g=GM/R2, where Mis the mass of the sphere without cavity]a)mg/2b)3mg/8c)mg/16d)None of theseCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics 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