The length of the second's hand in a watch is $1 \, cm$. The change in velocity of its tip in $15 \, seconds$ is:

$A$ wheel rotates with a constant angular acceleration. The initial angular velocity is zero. It covers an angular displacement of ${\theta _1}$ in the first $2 \, s$ and ${\theta _2}$ in the next $2 \, s$. Then,the ratio $\frac{{\theta _1}}{{\theta _2}}$ is equal to:

Certain neutron stars are believed to be rotating at about $1 \, rev/sec$. If such a star has a radius of $20 \, km$,the acceleration of an object on the equator of the star will be:

$A$ car wheel is rotating at $1200$ revolutions per minute. On pressing the accelerator,it reaches $4500$ revolutions per minute in $10 \, s$. The angular acceleration of the wheel is:

An object moves along a circle with normal acceleration proportional to $t^\alpha$,where $t$ is the time and $\alpha$ is a positive constant. The power developed by all the forces acting on the object will have time dependence proportional to

$A$ particle is revolving in a circle of radius $2 \ m$ with angular velocity $\omega = t^2 - 4t + 8 \ rad/s$. The time when the speed of the particle becomes $8 \ m/s$ is ......... $\sec$.