A mass $m$ is suspended from a spring of negligible mass. The spring is pulled a little and then released, so that mass executes S.H.M. of time period $T$. If the mass is increased by $m_0$, the periodic time becomes $\frac{5 \mathrm{~T}}{4}$. The ratio $\frac{\mathrm{m}_0}{\mathrm{M}}$

The three vector $\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}, \vec{B}=\hat{i}-3 \hat{j}+5 k$ and $\vec{C}=2 \hat{i}-\hat{j}+4 \hat{k}$ will form

Two identical long parallel wires carry currents ' $\mathrm{I}_1$ ' and ' $\mathrm{I}_2$ ' such that $\mathrm{I}_1>\mathrm{I}_2$. When the currents are in the same direction, the magnetic field at a point midway between the wires is $8 \times 10^{-6} \mathrm{~T}$. If the direction of $\mathrm{I}_2$ is reversed, the field becomes $3.2 \times 10^{-5} \mathrm{~T}$. The ratio of $\mathrm{I}_2$ to $\mathrm{I}_1$ is

A disc of mass 25 kg and radius 0.2 m is rotating at 240 r.p.m. A retarding torque brings it to rest in 20 second. If the torque is due to a force applied tangentially on the rim of the disc then the magnitude of the force is