$A$ boy throws a cricket ball from the boundary to the wicket keeper. If the frictional force due to air $f_a$ cannot be ignored,the forces acting on the ball at the position $X$ are represented by

Two bodies of mass $10 \ kg$ and $5 \ kg$ are moving in concentric circular orbits of radii $R$ and $r$ respectively such that their periods are same. The ratio between their centripetal acceleration is

$A$ particle is moving with velocity $\vec v = K(y\hat i + x\hat j)$ where $K$ is a constant. The general equation for its path is

$A$ point moves in the $x-y$ plane according to the law $x = 3 \cos 4t$ and $y = 3(1 - \sin 4t)$. The distance travelled by the particle in $2 \text{ s}$ is...........$m$ (where $x$ and $y$ are in meters).

If the position vector of a particle is $\vec{r} = -\cos t \hat{i} + \sin t \hat{j} - 18t \hat{k}$,then what is the magnitude of its acceleration?

The given diagram shows a straight length of tape being wound on to a reel. The reel is rotating about a fixed axis with constant angular velocity and its radius is increasing at a steady rate. Which graph correctly shows the variation with time of the speed $v$ at which the tape moves towards the roll?