A small body of mass $m$ slides down from the top of a hemisphere of radius $r$. The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is
$\frac{3}{2}r$
$\frac{2}{3}r$
$\frac{1}{2}g{t^2}$
$\frac{{{v^2}}}{{2g}}$
A stone is tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u.$ The magnitude of the change in its velocity as it reaches a position where the string is horizontal is
A projectile is given an initial velocity of $(\hat i+2\hat j)\,m/ s$ where $\hat i$ is along the ground and $\hat j$ is along the vertical. If $g = 10\,m/s^2,$ the equation of its trajectory is
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 ball is rolled off the edge of a horizontal table at a speed of $4\, m/s$. It hits the ground after $0.4\, sec$. Which statement given below is true?