A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is ..............  $\mathrm{m} / \mathrm{s}$

The potential energy of a body of mass $m$ is:
                      $U = ax + by$
Where $x$ and $y$ are position co-ordinates of the particle. The acceleration of the particle is

A particle of mass $M$ is moving in a horizontal circle ofradius $R$ with uniform speed $v$. When it moves from one point to a diametrically opposite point, its
 

$A$ man who is running has half the kinetic energy of the boy of half his mass. The man speeds up by $1 \, m/s$ and then has the same kinetic energy as the boy. The original speed of the man was

A mass of $0.5\, kg$ moving with a speed of $1.5\, m/s$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k=50\,N/m$. The maximum compression of the spring would be ................. $\mathrm{m}$

A body of mass $2\, kg$ moving with a velocity of $3\, m/sec$ collides head on with a body of mass $1\, kg$ moving in opposite direction with a velocity of $4\, m/sec$. After collision, two bodies stick together and move with a common velocity which in $m/sec$ is equal to