A $4 \,kg$ mass and a $1\, kg$ mass are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is
$1:2$
$1:1$
$2:1$
$4:1$
The bob of a simple pendulum (mass m and length $ l$) dropped from a horizontal position strikes a block of the same mass elastically placed on a horizontal frictionless table. The K.E. of the block will be
A bomb of mass $3.0\, Kg$ explodes in air into two pieces of masses $2.0 \,kg$ and $1.0\, kg$. The smaller mass goes at a speed of $80 m/s$.The total energy imparted to the two fragments is ............. $kJ$
A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$-axis. Its kinetic energy $K$ changes with time as $dK / dt =\gamma$ t, where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?
$(A)$ The force applied on the particle is constant
$(B)$ The speed of the particle is proportional to time
$(C)$ The distance of the particle from the origin increases linearly with time
$(D)$ The force is conservative
Define kinetic energy. Give its unit and dimensional formula and mention works by using it.
A projectile is fired with $KE$ of $1\,kJ$. If the range is maximum, .......... $J$ is its $KE$ at the highest point.