A bob is whirled in a horizontal plane by means of a string with an initial speed of $\omega \mathrm{rpm}$. The tension in the string is $T$. If speed becomes $2 \omega$ while keeping the same radius, the tension in the string becomes:

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2$ sec, it rotates through an angle ${\theta _1}$. In the next $2$ sec, it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}\over{\theta _1}$ is

An aircraft executes a horizontal loop with a speed of $150\, m/s$ with its wings banked at an angle of $12^o$. The radius of the loop is ..........  $km$ $(g = 10\, m/s^2 \; and\; \tan 12^o = 0.2125)$

A stone tied to the end of a string $80\; cm$ long is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $25\; s$, what is the magnitude and direction of acceleration of the stone ?

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 motor cyclist going round in a circular track at constant speed has