Two solid spheres of iron have radii in the r | vedclass

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

Question

(D) The moment of inertia $I$ of a solid sphere is given by $I = \frac{2}{5} mr^{2}$.Since the spheres are made of the same material (iron), their den

Vedclass · Accepted Answer

$1 : 32$

Vedclass · Answer

(D) The moment of inertia $I$ of a solid sphere is given by $I = \frac{2}{5} mr^{2}$.Since the spheres are made of the same material (iron), their density $d$ is the same.The mass $m$ of a sphere is given by $m = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi r^{3} d$.Substituting the expression for mass into the moment of inertia formula:$I = \frac{2}{5} (\frac{4}{3} \pi r^{3} d) r^{2} = \frac{8}{15} \pi d r^{5}$.This shows that $I \propto r^{5}$.Given the ratio of radii $r_{1} : r_{2} = 1 : 2$, the ratio of their moments of inertia is:$\frac{I_{1}}{I_{2}} = (\frac{r_{1}}{r_{2}})^{5} = (\frac{1}{2})^{5} = \frac{1}{32}$.Therefore, the ratio is $1 : 32$.

Two solid spheres of iron have radii in the ratio $1 : 2$. Their moments of inertia will be in the ratio

Similar Questions

The ratio of masses and radii of two circular rings are $1 : 2$ and $2 : 1$ respectively. What is the ratio of their moments of inertia about their central axes?

$A$ thin rod of mass $M$ and length $L$ is bent at its midpoint $A$ such that it forms an angle of $60^{\circ}$. What is the moment of inertia about an axis passing through the midpoint $A$ and perpendicular to the plane of the rod?

Two discs of same mass and same thickness have densities as $17 \, g/cm^3$ and $51 \, g/cm^3$. The ratio of their moment of inertia about their central axes is .........

Define moment of inertia,write its unit and dimensional formula.

$A$ thin uniform wire of mass $m$ and linear mass density $\rho$ is bent in the form of a circular loop. The moment of inertia of the loop about its diameter is

Vedclass Test Series

Exam Paper Generator

Online Exam Module