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
$y = x -5x^2$
$y =2 x -5x^2$
$4y = 2x -5x^2$
$4y = 2x -25x^2$
A ball is projected with velocity $V_0$ at an angle of elevation $30^o $ . Mark the correct statement
A body of mass $m\, kg$ is rotating in a vertical circle at the end of a string of length $r$ metre. The difference in the kinetic energy at the top and the bottom of the circle is
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
Two seconds after projection a projectile is travelling in a direction inclined at $30^o$ to horizontal, after one more second it is travelling horizontally. What is the magnitude and direction of its velocity at initial point
A particle does uniform circular motion in a horizontal plane. The radius of the circle is $20$ cm. The centripetal force acting on the particle is $10\, N$. It's kinetic energy is ........ $J$