Two charged particles $A$ and $B$ of masses $m$ and $2 m$, charges $2 q$ and $3 q$ respectively moving with same velocity enter a uniform magnetic field such that both the particles make same angle ( $<90^{\circ}$ ) with the direction of the magnetic field. Then, the ratio of pitches of the helical paths of the particles $A$ and $B$ is

A particle of charge 2 C is moving with a velocity of $(3 \hat{\mathbf{i}}+4 \hat{\mathrm{j}}) \mathrm{ms}^{-1}$ in the presence of magnetic and electric fields. If the magnetic field is $(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \mathrm{T}$ and the electric field is $(-2 \hat{\mathbf{k}}) \mathrm{NC}^{-1}$, then the Lorentz force on the particle is

A rectangular coil of 400 turns and $10^{-2} \mathrm{~m}^2$ area, carrying a current of 0.5 A is placed in a uniform magnetic field of IT such that the plane of the coil makes an angle of $60^{\circ}$ with the direction of the magnetic field. The initial moment of force acting on the coil in $\mathrm{N}-\mathrm{m}$ is

A square loop of side $a$ and carrying a current $I$ is suspended from an insulating hanger of a spring balance as shown in figure. The transverse magnetic field $B$ directed into the paper occurs only at the bottom side of the loop. When direction of current in the loop is reversed, the change in the reading of spring balance is