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 particle has initial velocity $(3\hat i + 4\hat j$$ ) $ and has acceleration $(0.4\,\hat i + 0.3\,\hat j)$ . Its speed after $10\,s$ is
If the instantaneous velocity of a particle projected as shown in figure is given by $v =a \hat{ i }+(b-c t) \hat{ j }$, where $a, b$, and $c$ are positive constants, the range on the horizontal plane will be
A particle is projected with a velocity $v$ such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where $g$ is acceleration due to gravity)
A projectile is thrown into space so as to have maximum horizontal range $R$. Taking the point of projection as origin, the coordinates of the points where the speed of the particle is minimum are-