A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by $1\,m/s$ so as to have same K.E. as that of the boy. The original speed of the man will be
$\sqrt 2 \,m/s$
$(\sqrt 2 - 1)\,m/s$
$\frac{1}{{(\sqrt 2 - 1)}}m/s$
$\frac{1}{{\sqrt 2 }}m/s$
The kinetic energy $k$ of a particle moving along a circle of radius $R$ depends on the distance covered $s$ as $k = a{s^2}$ where $a$ is a constant. The force acting on the particle is
If the linear momentum is increased by $50\%$, the kinetic energy will increase by ............. $\%$
The kinetic energy acquired by a mass $m$ in travelling a certain distance $d$ starting from rest under the action of a constant force is directly proportional to
A shell of mass $200\, gm$ is ejected from a gun of mass $4\, kg$ by an explosion that generates $1.05\, kJ$ of energy. The initial velocity of the shell is .............. $\mathrm{ms}^{-1}$
If the linear momentum is increased by $5\%$, the kinetic energy will increase by.......$\%$