Embibe Experts Solutions for Chapter: Circular Motion, Exercise 3: Exercise-3

A car of mass $1000 \mathrm{kg}$ negotiates a banked curve of radius $90 \mathrm{m}$ on a frictionless road. If the banking angle is $45°$, the speed of the car is:

A car of mass $m$ is moving on a level circular track of radius $R$. If ${\mu }_s$ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by:

In the given figure, $\alpha =15 \mathrm{m} {\mathrm{s}}^{-2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R=2.5 \mathrm{m}$ at a given instant of time. The speed of the particle is

A body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) Just completes a vertical circle of diameter $AB=D$. The height $h$ is equal to

A point $P$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of '$P$' is such that it sweeps out a length $s=t^3+5$, where $s$ is in metres and $t$ is in seconds. The radius of the path is $20 \mathrm{m}$. The acceleration of 'P' when $t=2 \mathrm{s}$ is nearly-

A particle is moving with a uniform speed in a circular orbit of radius $R$ in a central force inversely proportional to the $n^{th}$ power of $R.$ If the period of rotation of the particle is $T,$ then :

Two particles $A, B$ are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angular speed $\omega$. At $t=0$, their positions and direction of motion are shown in the figure.

The relative velocity ${\overrightarrow{v}}_A-{\overrightarrow{v}}_B$ at $t=\frac{\pi }{2\mathrm{\omega }}$ is

The position vector of a particle $\overrightarrow{R}$ as a function of time is given by $\overrightarrow{R}=4\sin \left(2\mathrm{\pi }t\right)\hat{\mathrm{i}}+4\cos \left(2\mathrm{\pi }t\right)\hat{\mathrm{j}}$ where $R$ is in meters, $t$ is seconds and $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ denote unit vectors along $x$- and $y$ directions, respectively. Which one of the following statements is wrong for the motion of particle