A metal ball of $$20 \mathrm{~g}$$ is projected at an angle $$30^{\circ}$$ with the horizontal with an initial velocity $$10 \mathrm{~ms}^{-1}$$. If the mass and angle of projection are doubled keeping the initial velocity the same, the ratio of the maximum height attained in the former to the latter case is :

A body is moving along a circular path of radius '$$r$$' with a frequency of revolution numerically equal to the radius of the circular path. What is the acceleration of the body if radius of the path is $$\left(\frac{5}{\pi}\right) m$$ ?

One end of the string of length $l$ is connected to a particle of mass $$m$$ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed $$v$$, the net force on the particle (directed towards centre) will be ( $$T$$ represents the tension in the string)

When a car of mass $$m$$ is moving with speed $$v$$ along a circle of radius $$r$$ on a level road, the centripetal force is provided by $$f$$, where $$f$$ denotes

($$\mu_s$$ $$\to$$ coefficient of friction, N $$\to$$ normal reaction)