A wheel completes $2000$ revolutions to cover the $9.5\, km$. distance. then the diameter of the wheel is

A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the 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 horizontal curve on $a$ racing track is banked at a $45^o $ angle. When a vehicle goes around this curve at the curve’s safe speed (no friction needed to stay on the track), what is its centripetal acceleration?

For particle $P$ revolving round the centre $O$ with radius of circular path $r$ and angular velocity $\omega$, as shown in below figure, the projection of $OP$ on the $x$-axis at time $t$ is $.................$.

The angular speed of a fly wheel making $120$ revolutions/minute is

A particle moves in a circular path of radius $r$ with speed $v.$ It then increases its speed to $2\,v$ while travelling along the same circular path. The centripetal acceleration of the particle has changed by a factor of