A particle is moving in $x y$-plane in a circular path with centre at origin. If at an instant the position of particle is given by $\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$, then velocity of particle is along .......
$\frac{1}{\sqrt{2}}(\tilde{i}-\hat{j})$
$\frac{1}{\sqrt{2}}(\hat{j}-\hat{i})$
$\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$
Elther $(a)$ or $(b)$
A ball is moving uniformly in a circular path of radius $1 m$ with a time period of $1.5 \,s$. If the ball is suddenly stopped at $t=8.3 \,s$, the magnitude of the displacement of the ball with respect to its position at $t=0 \,s$ is closest to .......... $m$
A car goes around uniform circular track of radius $R$ at a uniform speed $v$ once in every $T$ seconds. The magnitude of the centripetal acceleration is $a_c$. If the car now goes uniformly around a larger circular track of radius $2 R$ and experiences a centripetal acceleration of magnitude $8 a_c$. Then, its time period is
A car is moving with a uniform speed on a level road. Inside the car there is a balloon filled with helium and attached to a piece of string tied to the floor. The string is observed to be vertical. The car now takes a left turn maintaining the speed on the level road. The balloon in the car will
Three point particles $P, Q, R$ move in circle of 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 rad/ sec) of $P, Q$ and $R$ are $5\pi , 2\pi$ & $3\pi$ respectively, in the same sense. the number of times $P$ and $Q$ meet in that time interval is:
A particle $P$ is sliding down a frictionless hemispherical bowl. It passes the point $A$ at $t = 0$. At this instant of time, the horizontal component of its velocity is $v$. A bead $Q$ of the same mass as $P$ is ejected from $A$ at $t = 0$ along the horizontal string $AB$ (see figure) with the speed $v$. Friction between the bead and the string may be neglected. Let ${t_P}$ and ${t_Q}$ be the respective time taken by $P$ and $Q$ to reach the point $B$. Then