Embibe Experts Solutions for Chapter: Rotational Motion, Exercise 1: Level 1

A uniform square plate $ABCD$ has a mass of $10 \mathrm{kg}.$ If two point masses of $3 \mathrm{kg}$ each are placed corners $C$ and $D$ as shown in the adjoining figure, then the centre of mass shifts to the point which lies on -

A body whose moment of inertia is $3 \mathrm{kg} {\mathrm{m}}^2$ is at rest. It is rotated for $20 \mathrm{s}$ by a torque of $6 \mathrm{N} \mathrm{m}$, angular displacement of the body will be

The moment of inertia of a disc about axis $O$$O\text{'}$ is $Nm{r}^2$. Axis is in the plane of disc and tangential. Then the value of $N$ is:

The moment of inertia of a metre scale of mass $0.6 \mathrm{kg}$ about an axis perpendicular to the scale and located at the $20 \mathrm{cm}$ position on the scale is $n$ $\mathrm{kg} m^2$ (Breadth of the scale is negligible). The value of $n$ is

The moment of inertia of a hollow cubical box of mass $M$ and side length $a$, about an axis passing through centres of two opposite faces, is equal to $\frac{xM{a}^2}{18}$. The value of $x$ is

A thin rod of length $L$ and mass $M$ is bent at the middle point $O$ as shown in the figure. Consider an axis passing through two middle the point $O$ and perpendicular to the plane of the bent rod. Then the moment of inertia about this axis is

Two rotating bodies $A$ and $B$ of masses $m$ and $2 \mathrm{m}$ with moments of inertia $I_{\mathrm{A}}$ and $I_{\mathrm{B}}$ $\left(I_{\mathrm{B}}>I_{\mathrm{A}}\right)$ have equal kinetic energy of rotation. If $L_{\mathrm{A}}$ and$L_{\mathrm{B}}$ be their angular momenta respectively, then $\frac{L_{\mathrm{B}}}{L_{\mathrm{A}}}>x$. Find $x$.

The moments of inertia of two rotating bodies $A$ and $B$ are $I_A$ and $I_B\left(I_A>I_B\right)$ and their angular momentum are equal. If their kinetic energies be $K_A$ and $K_d,$ respectively, then