Embibe Experts Solutions for Chapter: Circular Motion, Exercise 4: Exercise-4

Three point particles $P$, $Q$ and $R$ move in a circle of the radius $r$ with different but constant speeds. They start moving at $t=0$ from their initial positions as shown in the figure. The angular velocities (in $\mathrm{rad} {\sec }^{-1}$) of $P$, $Q$ and $R$ are $5\mathrm{\pi }$, $2\mathrm{\pi }$ and $3\mathrm{\pi }$, respectively, in the same sense. The time interval after which they all meet is

A particle of mass $m$ is suspended from a fixed point $O$ by a string of length $\ell$. It is displaced by an angle $\mathrm{\theta }\left(\mathrm{\theta }<90°\right)$ from the equilibrium position and released from there at $t=0$. The graph, which shows the variation of the tension $T$ in the string with time $t$, maybe:

A particle moves along an arc of a circle of radius $R$. Its velocity depends on the distance covered $s$ as $v=a\sqrt{s}$, where $a$ is a constant then the angle $\alpha$ between the vector of the total acceleration and the vector of velocity as a function of $s$ will be

Two particles $P$ and $Q$ start their journey simultaneously from point $A$. $P$ moves along a smooth horizontal circular wire with diameter $AB$. $Q$ moves along a curved smooth track. $Q$ has sufficient velocity at $A$ to reach $B$ always remaining in contact with the curved track. At $A$, the horizontal component of velocity of $Q$ is same as the velocity of $P$ along the wire. The plane of motion is vertical. If $t_1,t_2$, are times taken by $P$ and $Q$ respectively to reach $B$ then (Assume velocity of $P$ is constant)

A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid at the other end is

A wire, which passes through the hole is a small bead, is bent in the form of a quarter of a circle. The wire is fixed vertically on the ground as shown in the figure. The bead is released from near the top of the wire, and it slides along the wire without friction. As the bead moves from $A$ to $B$, the force it applies on the wire is