A body constrained to move along $y-$ axis is subjected to a constant force $\vec F =  - \hat i + 2\hat j + 3\hat k\,N$ The work done by this force in moving the body a distance of $4\, m$ along $y-$ axis is ............... $\mathrm{J}$

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

Three particles of masses $10g, 20g$ and $40g$ are moving with velocities $10\widehat i,10\widehat j$ and  $10\widehat k$ $m/s$ respectively. If due to some mutual interaction, the first particle comes to  rest and the velocity of second particle becomes $\left( {3\widehat i + 4\widehat j\,\,} \right)\, m/s$, then the velocity of third particle is

$A$ & $B$ are blocks of same mass $m$ exactly equivalent to each other. Both are  placed on frictionless surface connected by one spring. Natural length of spring is $L$  and force constant $K$. Initially spring is in natural length. Another equivalent block $C$  of mass $m$ travelling at speed $v$ along line joining $A$ & $B$ collide with $A$. In  ideal condition maximum compression of spring is :-

Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{{3{t^2}}}{2}$ $watt$ . Here, $t$ is in $seconds$ . If velocity of particle at $t = 0$ is $v = 0$, the velocity of particle at time $t = 2\, s$ will be ............ $\mathrm{m}/ \mathrm{s}$

Which one of the following statement does not hold good when two balls of masses ${m_1}$ and ${m_2}$ undergo elastic collision