SATHEE: Rotational Motion Question 10

Rotational Motion Question 10

Question: One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $I_{A}$ and $I_{B}$ such that where $d_{A}$ and $d_{B}$ are their densities.

[AIEEE 2004]

Options:

A) $I_{A} = I_{B}$

B) $I_{A} > I_{B}$

C) $I_{A} < I_{B}$

D) $\frac{I_{A}}{I_{B}} < \frac{d_{A}}{d_{B}}$

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Let same mass and same outer radii of solid sphere and hollow sphere are M and R, respectively.

The moment of inertia of solid sphere A about its diameter $l_{A} = \frac{2}{5} M R^{2}$ …(i)

Similarly, the moment of inertia of hollow sphere (spherical shell) B about its diameter $l_{B} = \frac{2}{3} M R^{2}$ …(ii)

It is clear from Eqs.

(i) and (ii), $l_{A} < l_{B}$ .

Alternatively We can say that the object which has mass at greater distance will have higher moment of inertia as $l = m r^{2}$ .

So, hollow sphere has large $l$ , because it has mass only on its circumference.

Rotational Motion Question 10

Question: One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $I_{A}$ and $I_{B}$ such that where $d_{A}$ and $d_{B}$ are their densities.

Options:

Answer:

Solution:

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Rotational Motion Question 10

Question: One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively IA and IB such that where dA and dB are their densities.

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $I_{A}$ and $I_{B}$ such that where $d_{A}$ and $d_{B}$ are their densities.