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

The centre of mass of triangle shown in figure has coordinates

A uniform solid cone of height $40 \mathrm{cm}$ is shown in the figure. The distance of the centre of mass of the cone from point $B$ (centre of the base) is:

A uniform disc of radius $R$ had initial angular velocity ${\omega }_0$ and then gently placed on a rough horizontal surface at time $t=0$, with its plane horizontal. The friction coefficient between the disc and the horizontal surface is $\mu$. Then

A ring of mass $\mathrm{m}$ and radius $R$ is placed on a rough horizontal surface (co-efficient of friction $\mu$) with velocity of C.M. $V_0$ and angular speed $\frac{2V_0}{R}$ as shown in figure. Initially the ring is rolling with slipping but attains pure rolling motion after some time $t$. Then

Two men of masses $60 \mathrm{kg}$ and $80 \mathrm{kg}$ are at the two ends of a slab of mass $160 \mathrm{kg}$ as shown in figure. The horizontal surface is smooth. If the men interchange their positions on the slab, then displacement (in $\mathrm{cm}$) of the slab is approximately (closest integer)

From a uniform disk of radius $R$, an equilateral triangle of side $\sqrt{3}R$ is removed. The position of centre of mass now is $\left(0,N\right)$, then value of $N$ is ____ unit. (Given $R=12$ units)

A uniform bar with mass $m=16\mathrm{kg}$ lies symmetrically across two rapidly rotating fixed rollers, $A$ and $B$ with distance '$\ell =8\mathrm{m}$' between the bars centre of mass and each roller. The rollers whose direction of rotation are shown in figure slip against the bar with coefficient of friction $\mu =0.2$. Suppose the bar is displaced horizontally by a small distance '$x$' and then released, the time period of oscillation in sec is.

A cylinder of mass $M=2 \mathrm{kg }$and radius $R=12 \mathrm{cm}$ lies on a plank of the same mass as shown in the figure. The surface between plank and ground is smooth but there is friction between cylinder and plank. If the coefficient of friction between the cylinder and the plank is $\mu =0.4$, then what maximum initial compression (in $\mathrm{cm}$) can be given to the spring such that the cylinder moves without slipping with respect to the plank? [Given, $k=200 \mathrm{N} {\mathrm{m}}^{-1}$]