The centre of mass of two masses $m$ and $m'$ moves by a distance $\frac{x}{5}$ when mass $m$ is moved by a distance $x$ and $m'$ is kept fixed. The ratio $\frac{m'}{m}$ is

Two full turns of the circular scale of a screw gauge cover a distance of $1\,mm$ on the main scale. The total number of divisions on the circular scale is $50$. Further,it is found that the screw gauge has a zero error of $+0.03\,mm$. While measuring the diameter of a thin wire,a student notes the main scale reading of $3\,mm$ and the number of the circular scale division in line with the main scale is $35$. The diameter of the wire is .......... $mm$.

The balancing length for a cell is $560 \, cm$ in a potentiometer experiment. When an external resistance of $10 \, \Omega$ is connected in parallel to the cell, the balancing length changes by $60 \, cm$. The internal resistance of the cell in ohms is:

The energy of a hydrogen atom in its ground state is $-13.6 \,eV$. The energy of the level corresponding to $n=5$ is ........ $eV$.

The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is:

The $PV$ diagram shows four different possible reversible processes performed on a monatomic ideal gas. Process $A$ is isobaric (constant pressure). Process $B$ is isothermal (constant temperature). Process $C$ is adiabatic. Process $D$ is isochoric (constant volume). For which process(es) does the temperature of the gas decrease?