A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will

particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec a\, = \,(4\hat i + 3\hat j)\,\,m/{s^2}$ and $\vec P\, = \,(8\hat i\, - \,6\hat j)\,kg\, - \,m/s$ . The motion of the particle is

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 $.................$.

Which of the following quantities remains constant during uniform circular motion?

A cyclist starts from centre 0 of a circular park of radius $1\, km$ and, moves along the path $OPRQO$ as shown in figure.

If he maintains constant speed of $10\, ms^{-1}$, what is his acceleration at point $R$ in magnitude and direction ?

The net applied force on a body in uniform circular motion should always be