An aeroplane executes a horizontal loop at a speed of $720 \text{ km/h}$ with its wings banked at $45^{\circ}$. What is the radius of the loop (in $\text{ km}$)? Take $g = 10 \text{ m/s}^2$.

$A$ body of mass $100 \, g$ is projected at an angle of $30^\circ$ with the horizontal with a velocity of $20 \, m \, s^{-1}$. What is the change in its momentum at the maximum height in $kg \, m \, s^{-1}$?

The initial velocity of a projectile is $\vec{u} = (4\hat{i} + 3\hat{j})\,m/s$. It is moving with uniform acceleration $\vec{a} = (0.4\hat{i} + 0.3\hat{j})\,m/s^2$. The magnitude of its velocity after $10\,s$ is.........$m/s$.

Two bodies of mass $10 \, kg$ and $5 \, kg$ are moving in concentric orbits of radii $R$ and $r$ such that their periods are the same. What is the ratio of their centripetal accelerations?

The second's hand of a watch has a length of $6\,cm$. The speed of the end point and the magnitude of the difference of velocities at two perpendicular positions will be:

The velocity of a particle moving in a curvilinear path in a horizontal $X-Y$ plane varies with time as $\vec{v} = (2t\hat{i} + t^2\hat{j}) \ m/s$. Here,$t$ is in seconds. At $t = 1 \ s$: