If a solid sphere and a solid cylinder of the | vedclass

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

Question

(A) The moment of inertia of a solid sphere is $I_{sphere} = \frac{2}{5} M_1 R^2$,where $M_1 = \frac{4}{3} \pi R^3 \rho$.So,$I_{sphere} = \frac{2}{5}

Vedclass · Accepted Answer

Solid sphere

Vedclass · Answer

(A) The moment of inertia of a solid sphere is $I_{sphere} = \frac{2}{5} M_1 R^2$,where $M_1 = \frac{4}{3} \pi R^3 \rho$.So,$I_{sphere} = \frac{2}{5} (\frac{4}{3} \pi R^3 \rho) R^2 = \frac{8}{15} \pi \rho R^5$.The moment of inertia of a solid cylinder is $I_{cylinder} = \frac{1}{2} M_2 R^2$,where $M_2 = \pi R^2 L \rho$. Given $L = R$,$M_2 = \pi R^3 \rho$.So,$I_{cylinder} = \frac{1}{2} (\pi R^3 \rho) R^2 = \frac{1}{2} \pi \rho R^5$.Comparing the two: $\frac{I_{sphere}}{I_{cylinder}} = \frac{\frac{8}{15} \pi \rho R^5}{\frac{1}{2} \pi \rho R^5} = \frac{16}{15}$.Since $\frac{16}{15} > 1$,it follows that $I_{sphere} > I_{cylinder}$.

If a solid sphere and a solid cylinder of the same radius and density rotate about their own axes,which one will have a greater moment of inertia? (Assume $L=R$ for the cylinder)

Similar Questions

The expression $1+x \log _e a+\frac{x^2}{2 !}(\log _e a)^2+\frac{x^3}{3 !}(\log _e a)^3+\ldots$ for $a>0, x \in R$ is equal to:

$A$ body is projected at an angle $\theta$ so that its range is maximum. If $T$ is the time of flight,then the value of maximum range is (acceleration due to gravity $= g$)

$A$ vessel contains a mixture of one mole of oxygen and two moles of nitrogen at $300 \ K$. The ratio of the average rotational kinetic energy per $O_2$ molecule to that per $N_2$ molecule is

An inductive circuit contains a resistance of $10\,\Omega$ and an inductance of $2.0\,H$. If an $AC$ voltage of $120\,V$ and frequency $60\,Hz$ is applied to this circuit,the current would be nearly ................$A$.

From the ground state electronic configuration of the elements given below,pick the one with the highest value of second ionisation energy.

Vedclass Test Series

Exam Paper Generator

Online Exam Module