The moment of inertia of a sphere (mass M and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given,the moment of inertia $(MOI)$ of a sphere about its diameter is $I = \frac{2}{5} M R^{2}$.In the given arrangement,two spheres are placed su

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(D) Given,the moment of inertia $(MOI)$ of a sphere about its diameter is $I = \frac{2}{5} M R^{2}$.In the given arrangement,two spheres are placed such that their centers lie on the axis $XX'$. For these two spheres,the axis $XX'$ passes through their diameters. Thus,the $MOI$ for each of these two spheres is $I = \frac{2}{5} M R^{2}$.The other two spheres are placed such that their centers are at a distance $R$ from the axis $XX'$. Using the parallel axis theorem,the $MOI$ of each of these two spheres about the axis $XX'$ is $I' = I_{cm} + M R^{2} = \frac{2}{5} M R^{2} + M R^{2} = \frac{7}{5} M R^{2}$.Since $I = \frac{2}{5} M R^{2}$,we have $M R^{2} = \frac{5}{2} I$. Therefore,$I' = \frac{7}{5} 	imes (\frac{5}{2} I) = \frac{7}{2} I$.The total moment of inertia of the system is $I_{total} = 2 	imes I + 2 	imes I' = 2I + 2 	imes (\frac{7}{2} I) = 2I + 7I = 9I$.

The moment of inertia of a sphere (mass $M$ and radius $R$) about its diameter is $I$. Four such spheres are arranged as shown in the figure. The moment of inertia of the system about the axis $XX'$ will be (in $,I$)

Similar Questions

Which one of the following statements is wrong?

$M_p$ denotes the mass of a proton and $M_n$ denotes the mass of a neutron. $A$ given nucleus,of binding energy $B$,contains $Z$ protons and $N$ neutrons. The mass $M(N, Z)$ of the nucleus is given by ($c$ is the velocity of light):

The sum total of all the chemical reactions occurring in our body is known as

Which of the following is used for making optical instruments?

Sodium reacts more vigorously with water than lithium because ....

Vedclass Test Series

Exam Paper Generator

Online Exam Module