After on head on elastic collision between two balls of equal masses , one is observed to have a speed of $3\, m/s$ along positive $x$ -axis and the other has a speed of $2\, m/s$ along negative $x$ -axis. The original velocities of the balls are
$-2 \,m/s$ and $+3 \,m/s$
$+2 \,m/s$ and $+3 \,m/s$
$-3 \,m/s$ and $+2 \,m/s$
$+3 \,m/s$ and $-2 \,m/s$
A bomb of mass $9\, kg$ explodes into two pieces of masses $3\, kg$ and $6\, kg$. The velocity of mass $3\, kg$ is $16\, m/s$. The $KE$ of mass $6\, kg$ (in joule) is
A particle moves along the $x-$ axis from $x = 0$ to $x = 5\,m$ under the influence of a force $F$ (in $N$ ) given by $F = 3x^2 -2x + 7$ . Calculate the work done by this force .............. $\mathrm{J}$
The potential energy of a diatomic molecule is given by $U = \frac{A}{{{r^{12}}}} - \frac{B}{{{r^6}}}$ . $A$ and $B$ are positive constants. The distance $r$ between them at equilibrium is
A ball of mass $M$ falls from a height $h$ on a floor. If co-efficient of restitution is $e$, the height attained by the ball after two rebounds is
A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is