A spring of force constant $K$ is first stretched by distance a from its natural length and then further by distance $b$. The work done in stretching the part $b$ is .............
$\frac{1}{2} K a(a-b)$
$\frac{1}{2} K a(a+b)$
$\frac{1}{2} K b(2 a+b)$
$\frac{1}{2} K b(a-b)$
A shell is fired from a canon with a velocity $V$ at an angle $\theta$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces come to rest. The speed of the other piece immediately after the explosion is
A $15\, g$ ball is shot from a spring gun whose spring has a force constant of $600\, N\, m$. The spring is compressed by $3\, cm$. The greatest possible velocity of the ball for this compression is ............. $\mathrm{m}/ \mathrm{s}$ $(g = 10\, m/s^2$)
A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to:
A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function of time is given by