The coordinates of a moving particle at any time $t$ are given by $x = a\, t^2$ and $y = b\, t^2$. The speed of the particle is

In the following cases,identify the source providing the centripetal force:
$(i)$ Motion of the Earth around the Sun.
$(ii)$ Motion of an electron around the nucleus.
$(iii)$ Motion of a vehicle on a horizontal curved road.

$A$ body is moving with velocity $30 \; m/s$ towards east. After $10 \; s$,its velocity becomes $40 \; m/s$ towards north. The average acceleration of the body is ...... $m/s^2$.

Which of the following is not a projectile?

If the radius of the circular path and the frequency of revolution of a particle of mass $m$ are doubled,then the change in its kinetic energy will be ($E_i$ and $E_f$ are the initial and final kinetic energies of the particle respectively). (in $E_i$)

$A$ particle of mass $M$ is moving in a horizontal circle of radius $R$ with uniform speed $v$. When the particle moves from one point to a diametrically opposite point,its