The $x-t$ graph of a particle moving along a straight line is shown in figure The distance-time graph of the particle is correctly shown by

A body slides down a frictionless track which ends in a circular loop of diameter $D$, then the minimum height $h$ of the body in term of $D$ so that it may just complete the loop, is

Two cars of masses $m_1$ & $m_2$ are moving along the circular paths of radius $r_1$ & $r_2$ respectively. Their speeds are such that they complete one round in same time. The ratio of angular speeds of two cars is

A particle is projected from a horizontal plane such that its velocity vector at time $t$ is given by $\vec v = a\hat i + (b - ct)\hat j$ . Its range on the horizontal plane is given by

An aircraft executes a horizontal loop with a speed of $150 \,m/s$ with its, wings banked at an angle of ${12^o }$. The radius of the loop is ..........  $km$. $(g = 10\,\,m/{s^2})$