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
$\frac{{ML{\omega ^2}}}{2}$
$ML{\omega ^2}$
$\frac{{M{\omega }L^2}}{2}$
$\frac{{M{L^2}{\omega ^2}}}{2}$
A cyclist is riding with a speed of $27 \;km/h.$ As he approaches a circular turn on the road of radius $80\; m$, he applies brakes and reduces his speed at the constant rate of $0.50\; m/s$ every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn ?
Two spheres $P$ and $Q$ of equal masses are attached to a string of length $2\,\, m$ as shown in figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant rate. What is the value of the ratio
$\left( {\frac{{{\text{Tension in the string between P and Q}}}}{{{\text{Tension in the string between P and O}}}}} \right)?$
A man is running with constant speed along a circular path of radius $2 \sqrt 2\, m$. He completes $1$ round in $10\, second$. Find instantaneous speed at $2.5 \,sec.$
The ratio of angular speeds of minute hand and hour hand of a watch is
A particle is tied to $20\, cm$ long string. It performs circular motion in vertical plane. What is the angular speed of particle when the tension in the string at the top is zero ......... $rad/sec$