$A$ body of mass $m$ moving with velocity $v$ collides head-on with another body of mass $2m$ which is initially at rest. The ratio of the kinetic energy of the colliding body before and after the collision will be: (in $:1$)

$A$ wheel with ten metallic spokes,each $0.50 \ m$ long,is rotated with a speed of $120 \ rev/min$ in a plane normal to the earth's magnetic field at the place. If the magnitude of the field is $0.4 \ G$,the induced $e.m.f.$ between the axle and the rim of the wheel is equal to:

The vectors $\vec{AB} = 3\hat{i} - 2\hat{j} + 2\hat{k}$ and $\vec{BC} = \hat{i} - 2\hat{k}$ are the adjacent sides of a parallelogram. The angle between its diagonals is

Which of the following is an amphoteric hydroxide?

$A$ magnet of length $10 \text{ cm}$ and magnetic moment $1 \text{ Am}^2$ is placed along side $AB$ of an equilateral triangle $ABC$. If the length of the side $AB$ is $10 \text{ cm}$,find the magnetic induction at the point $C$. (Given $\mu_0 = 4\pi \times 10^{-7} \text{ Hm}^{-1}$)

$A$ $4 \, kg$ mass and a $1 \, kg$ mass are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is