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Two spheres of same mass and radius are in contact with each other. If the moment of inertia of a sphere about its diameter is I, then the moment of inertia of both the spheres about the tangent at their common point would be -
- a)3I
- b)7I
- c)4I
- d)5I
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two spheres of same mass and radius are in contact with each other. If...
The moment of inertia of a sphere about its diameter is given as,
I=2/5 MR2
The moment of inertia of the sphere about the tangent is given as,
I′=2/5MR2+MR2
I′=7/5MR2
The total moment of inertia of both spheres about the common tangent is given as,
It=2I′
It=2×7/5MR2
It=7I
I=2/5 MR2
The moment of inertia of the sphere about the tangent is given as,
I′=2/5MR2+MR2
I′=7/5MR2
The total moment of inertia of both spheres about the common tangent is given as,
It=2I′
It=2×7/5MR2
It=7I
Most Upvoted Answer
Two spheres of same mass and radius are in contact with each other. If...
Moment of Inertia about Diameter
The moment of inertia of a solid sphere about its diameter is given by the formula:
I = (2/5) * m * r^2
where I is the moment of inertia, m is the mass of the sphere, and r is the radius of the sphere.
Moment of Inertia about Tangent
To find the moment of inertia of both spheres about the tangent at their common point, we can consider the two spheres as a single system. By the parallel axis theorem, the moment of inertia of a system of particles about an axis is equal to the sum of the individual moments of inertia of the particles about the same axis.
In this case, since the two spheres are in contact with each other, their common point of contact can be considered as the axis of rotation. Therefore, the moment of inertia of the system about the tangent at their common point is the sum of the individual moments of inertia of the spheres about their diameter:
I_total = I_sphere1 + I_sphere2
Since both spheres have the same mass and radius, their individual moments of inertia about their diameter are the same. Therefore, we can rewrite the equation as:
I_total = 2 * I
Final Thoughts
The moment of inertia of both spheres about the tangent at their common point is equal to twice the moment of inertia of a single sphere about its diameter:
I_total = 2 * I = 2 * (2/5) * m * r^2 = (4/5) * m * r^2
Therefore, the correct answer is option B: 7I.
The moment of inertia of a solid sphere about its diameter is given by the formula:
I = (2/5) * m * r^2
where I is the moment of inertia, m is the mass of the sphere, and r is the radius of the sphere.
Moment of Inertia about Tangent
To find the moment of inertia of both spheres about the tangent at their common point, we can consider the two spheres as a single system. By the parallel axis theorem, the moment of inertia of a system of particles about an axis is equal to the sum of the individual moments of inertia of the particles about the same axis.
In this case, since the two spheres are in contact with each other, their common point of contact can be considered as the axis of rotation. Therefore, the moment of inertia of the system about the tangent at their common point is the sum of the individual moments of inertia of the spheres about their diameter:
I_total = I_sphere1 + I_sphere2
Since both spheres have the same mass and radius, their individual moments of inertia about their diameter are the same. Therefore, we can rewrite the equation as:
I_total = 2 * I
Final Thoughts
The moment of inertia of both spheres about the tangent at their common point is equal to twice the moment of inertia of a single sphere about its diameter:
I_total = 2 * I = 2 * (2/5) * m * r^2 = (4/5) * m * r^2
Therefore, the correct answer is option B: 7I.
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Two spheres of same mass and radius are in contact with each other. If...
7I
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Two spheres of same mass and radius are in contact with each other. If the moment of inertia of a sphere about its diameter is I, then the moment of inertia of both the spheres about the tangent at their common point would be -a)3Ib)7Ic)4Id)5ICorrect answer is option 'B'. Can you explain this answer?
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