The energy liberated on complete fission of $1\, kg$ of $_{92}U^{235}$ is (Assume $200\, MeV$ energy is liberated on fission of $1$ nucleus).

$A$ vertical spring with force constant $k$ is fixed on a table. $A$ ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is

The correct relation between the degree of freedom $f$ and the ratio of specific heat $\gamma$ is -

Calculate the $pOH$ of a solution at $25\,^{\circ}C$ that contains $1 \times 10^{-10} \, M$ of hydronium ions,i.e.,$H_3O^{+}$.

The ratio of thermal conductivity of two rods of different materials is $5 : 4$. If the two rods have the same cross-sectional area and the same thermal resistance,what is the ratio of their lengths?

$A$ container of mass $m$ is pulled by a constant force $F$. Inside the container,a second block of the same mass $m$ is placed,connected to the wall by a massless spring of constant $k$. Initially,the spring is at its natural length. Find the velocity of the container at the instant when the compression in the spring is maximum for the first time.