A solid sphere and a solid cylinder of same m | vedclass

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

Question

(A) The moment of inertia $I$ of a body is given by $I = mk^2$,where $m$ is the mass and $k$ is the radius of gyration.For a solid sphere,the moment o

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) The moment of inertia $I$ of a body is given by $I = mk^2$,where $m$ is the mass and $k$ is the radius of gyration.For a solid sphere,the moment of inertia about its central axis is $I_{	ext{sph}} = \frac{2}{5}mR^2$.Equating this to $mk_{	ext{sph}}^2$,we get $k_{	ext{sph}} = \sqrt{\frac{2}{5}}R$.For a solid cylinder,the moment of inertia about its central axis is $I_{	ext{cyl}} = \frac{1}{2}mR^2$.Equating this to $mk_{	ext{cyl}}^2$,we get $k_{	ext{cyl}} = \frac{R}{\sqrt{2}}$.The ratio of the radii of gyration is $\frac{k_{	ext{sph}}}{k_{	ext{cyl}}} = \frac{\sqrt{2/5}R}{R/\sqrt{2}} = \sqrt{\frac{2}{5}} 	imes \sqrt{2} = \sqrt{\frac{4}{5}} = \frac{2}{\sqrt{5}}$.Comparing this with the given ratio $\frac{2}{\sqrt{x}}$,we find that $x = 5$.

$A$ solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively $(k_{\text{sph}} : k_{\text{cyl}})$ is $2 : \sqrt{x}$,then the value of $x$ is .............

Similar Questions

Two solid spheres ($A$ and $B$) are made of metals of different densities $\rho_A$ and $\rho_B$ respectively. If their masses are equal, the ratio of their moments of inertia $(I_B / I_A)$ about their respective diameter is

$A$ circular disc of radius $b$ has a hole of radius $a$ at its centre (see figure). If the mass per unit area of the disc varies as $\sigma(r) = \frac{\sigma_0}{r}$,then the radius of gyration of the disc about its axis passing through the centre is

Two iron solid discs of negligible thickness have radii $R_1$ and $R_2$ and moments of inertia $I_1$ and $I_2$,respectively. For $R_2 = 2 R_1$,the ratio of $I_1$ and $I_2$ would be $1 / x$,where $x = $ . . . . . . .

The ratio of the radius of gyration of a circular disc to that of a circular ring,each of the same mass and radius,about their respective central axes is:

Two rings of radius $R$ and $nR$ having different masses and made up of the same wire have the ratio of moment of inertia about an axis passing through the centre as $1 : 8$. The value of $n$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module