How many unit cells are present in $39 \ g$ of potassium that crystallises in body-centred cubic structure? [At. wt. of $K = 39$]

$A$ mass $M \text{ kg}$ is suspended by a weightless string. The horizontal force required to hold the mass at $60^{\circ}$ with the vertical is

In an optical fibre,the core and cladding are made with materials of refractive indices $1.5$ and $1.414$ respectively. To observe total internal reflection,what will be the range of the incident angle with the axis of the optical fibre?

$A$ complex compound of $Co^{3+}$ with molecular formula $CoCl_{x} \cdot yNH_3$ gives a total of $3$ ions when dissolved in water. How many $Cl^{-}$ ions satisfy both primary and secondary valencies in this complex?

The function $f(x) = |px - q| + r|x|,$ $x \in ( - \infty, \infty )$ where $p > 0, q > 0, r > 0$ assumes its minimum value only at one point if

An assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. At this instant,the springs are relaxed. The left mass is displaced to the left and the right mass is displaced to the right by the same distance and released. The resulting collision is elastic. The time period of the oscillations of the system is