$A$ force of $(3\hat i + 4\hat j)\, N$ acts on a body and displaces it by $(3\hat i + 4\hat j)\, m$. The work done by the force is ............. $J$.

$A$ sample of $0.1 \ g$ of water at $100^{\circ} C$ and normal pressure $(1.013 \times 10^5 \ N m^{-2})$ requires $54 \ cal$ of heat energy to convert to steam at $100^{\circ} C$. If the volume of the steam produced is $167.1 \ cc$,the change in internal energy of the sample is ....... $J$.

$A$ satellite is revolving very close to a planet of density $\rho$. The period of revolution of the satellite is

If $a = \hat{i} + \hat{j} + t \hat{k}$ and $b = \hat{i} + 2 \hat{j} + 3 \hat{k}$,then the values of $t$ for which $(a+b)$ and $(a-b)$ are perpendicular are:

$A$ cylindrical conductor of radius $R$ carries a current $i$. The value of the magnetic field at a point which is $R/4$ distance inside from the surface is $10 \ T$. Find the value of the magnetic field at a point which is $4R$ distance outside from the surface.