A solid sphere has mass M and radius R. Its m | vedclass

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

Question

(D) Concept: Application of the parallel axis theorem.The moment of inertia of a solid sphere about an axis passing through its centre is:$I_{	ext{cm

Vedclass · Accepted Answer

$\frac{13 MR^2}{20}$

Vedclass · Answer

(D) Concept: Application of the parallel axis theorem.The moment of inertia of a solid sphere about an axis passing through its centre is:$I_{	ext{cm}} = \frac{2}{5} MR^2$According to the parallel axis theorem,the moment of inertia $I$ about an axis parallel to the one passing through the centre of mass at a distance $d$ is given by:$I = I_{	ext{cm}} + Md^2$Here,the distance $d = \frac{R}{2}$.Substituting the values:$I = \frac{2}{5} MR^2 + M\left(\frac{R}{2}ight)^2$$I = \frac{2}{5} MR^2 + \frac{1}{4} MR^2$$I = \left(\frac{8 + 5}{20}ight) MR^2$$I = \frac{13}{20} MR^2$

$A$ solid sphere has mass $M$ and radius $R$. Its moment of inertia about a parallel axis passing through a point at a distance $\frac{R}{2}$ from its centre is

Similar Questions

The radius of gyration $K$ of a hollow sphere of mass $M$ and radius $R$ about an axis $XY$ is equal to $R$. The distance of that axis from the center of the sphere is $h$. The value of $h$ is

Consider a uniform square plate of side '$a$' and mass '$m$'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

According to the theorem of parallel axes $I = I_g + Md^2$,the graph between $I$ and $d$ will be

The moment of inertia of a thin uniform rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is

For a uniform rectangular sheet shown in the figure,the ratio of moments of inertia about the axes perpendicular to the sheet and passing through $O$ (the centre of mass) and $O'$ (corner point) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module