A particle gets displaced by $\Delta \,\vec r = \,(2\hat i + 3\hat j + 4\hat k)$ $m$ under the action of a force $\vec F = \,(7\hat i + 4\hat j + 3\hat k)$ The change in its kinetic energy is ............... $\mathrm{J}$

A bullet of mass $25\,g$ moving with a velocity of $200\,m/s$ is stopped within $5\,cm$ of the target. The average resistance offered by the target is ............... $\mathrm{kN}$

A block of mass $m = 10\,kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $0.05.$ When hit by a bullet of mass $50\,g$ moving with speed $v,$ that gets embedded in it, the block moves and comes to stop after moving a distance of $2\,m$ on the table. If a freely falling object were to acquire speed $\frac {v}{10}$ after being dropped from height $H,$ then neglecting energy losses and taking $g = 10\,ms^{-2},$ the value of $H$ is close to ................. $\mathrm{km}$

A $2\ kg$ object is floating at rest, acted upon by only force as indicated in figure. Find the total work done by the force in $3\ sec$ ..................... $\mathrm{J}$

State the importance of work energy theorem. Whether the work energy theorem is a scalar or a vector ?

The potential energy of a particle oscillating along $x-$ axis  is given as $U = 20 + (x - 2)^2$  where $U$  is in joules and $x$ in $meters$ . Total mechanical energy of the particle is $36\,\, J$ . Maximum kinetic energy of the particle is ................ $\mathrm{J}$