Embibe Experts Solutions for Chapter: Circular Motion, Exercise 2: Exercise - 2

Two particles $\mathrm{A}$ and $\mathrm{B}$ move anticlockwise with the same speed $v$ in a circle of radius $R$ and are diametrically opposite to each other. At $t=0, \mathrm{A}$ is imparted a tangential acceleration of constant magnitude $a_t=\frac{72v^2}{25\pi R}$ .If the time in which $\mathrm{A}$ collides with $\mathrm{B}$ is $\frac{5\pi R}{N_{1}v}$, the angle traced by $\mathrm{A}$ during this time is $\frac{11\pi }{{\mathrm{N}}_2}$, its angular velocity is $\frac{17v}{N_{3}R}$ and radial acceleration at the time of collision is $\frac{289 v^2}{5R{N}_4}$.Then calculate the value of $N_1 + N_2 + N_3 + N_4$.

Which of the following quantities may remain constant during the motion of an object along a curved path.

Assuming the motion of Earth around the Sun as a circular orbit with a constant speed of $30 \mathrm{km} {\mathrm{h}}^{-1}$.

A curved section of a road is banked for a speed $v$. If there is no friction between road and tyres of the car, then

A car of mass $m$ attempts to go on the circular road of radius $r$, which is banked for a speed of $36 \mathrm{km} {\mathrm{hr}}^{-1}$. The friction coefficient between the tyre and the road is negligible.

A particle is attached to an end of a rigid rod. The other end of the rod is hinged and the rod rotates always remaining horizontal. Its angular speed is increasing at constant rate. The mass of the particle is $m$. The force exerted by the rod on the particle is $\stackrel{\rightharpoonup }{F}$, then

A particle moves along a horizontal circle such that the radial force acting on it is directly proportional to square of time. Then choose the correct option :

A cylinder rotating at an angular speed of $50 \mathrm{rev}/\mathrm{s}$ is brought in contact with an identical stationary cylinder. Because of the kinetic friction, torques act on the two cylinders, accelerating the stationary one and decelerating the moving one. If the common magnitude of the angular acceleration and deceleration be $1 \mathrm{rev}/{\mathrm{s}}^2,$ then how much time (in seconds) it will take before the two cylinders have equal angular speed ?