Embibe Experts Solutions for Chapter: Rigid Body Dynamics, Exercise 2: Exercise 2

The moments of inertia of a non-uniform circular disc (of mass $M$ and radius $R$) about four mutually perpendicular tangents $AB, BC, CD, DA$ are $I_1,I_2,I_3$ and $I_4$, respectively (the square $ABCD$ circumscribes the circle.) The distance of the centre of mass of the disc from its geometrical centre is given by 

A rigid ball rolls without slipping on a surface shown below.

Which on the following is the most likely representation of the distance travelled by the ball vs time graph?

Which one of the following four graphs best depict the variation with $x$ of the moment of inertia $I$ of a uniform triangular lamina about an axis parallel to its base at a distance $x$ from it?

A uniform metal plate shaped like a triangle $ABC$ has a mass of $540 \mathrm{g}$. The length of the sides $AB,BC$ and $CA$ are $3 \mathrm{cm},5 \mathrm{cm}$ and $4 \mathrm{cm},$ respectively. The plate is pivoted freely about the point $A.$ What mass must be added to a vertex, so that the plate can hang with the long edge horizontal ?

A $V$ shaped rigid body has two identical uniform arms. What must be the angle between the two arms so that when the body is hung from one end, the other arm is horizontal?

A uniform ring of radius $R$ is moving on a horizontal surface with speed $v$ and then climbs up a ramp of inclination $30°$ to a height $h.$ There is no slipping in the entire motion. Then $h$ is

One end of a rod of length $L=1 \mathrm{m}$ is fixed to a point on the circumference of a wheel of radius $R=\frac{1}{\sqrt{3}} \mathrm{m}.$ The other end is sliding freely along a straight channel passing through the center $O$ of the wheel as shown in the figure below. The wheel is rotating with a constant angular velocity $\omega$ (in radian per second) about $O.$

The speed of the sliding end $P$ when $\theta =60°$ is

A solid cube of wood of side $2a$ and mass $M$ is resting on a horizontal surface as shown in the figure. The cube is free to rotate about a fixed axis $AB.$ A bullet of mass $m(<<M)$ and speed $v$ is shot horizontally at the face opposite to $ABCD$ at a height of $\frac{4a}{3}$ from the surface to impart the cube and angular speed $\omega .$ It strikes the face and embeds in the cube. Then $\omega$ is close to (note: the moment of inertia of the cube about an axis perpendicular to the face and passing through the center of mass is $\frac{2M{a}^2}{3}$.)