$A$ charged particle is moving in a uniform magnetic field. It penetrates a layer of lead and thereby loses half of its kinetic energy. What happens to the radius of curvature of its path?

Gauss is the unit of which physical quantity?

$A$ particle having a mass of $10^{-2} \, kg$ carries a charge of $5 \times 10^{-8} \, C$. The particle is given an initial horizontal velocity of $10^5 \, m/s$ in the presence of an electric field $\vec{E}$ and a magnetic field $\vec{B}$. To keep the particle moving in a horizontal direction,it is necessary that:
$(1)$ $\vec{B}$ should be perpendicular to the direction of velocity and $\vec{E}$ should be along the direction of velocity.
$(2)$ Both $\vec{B}$ and $\vec{E}$ should be along the direction of velocity.
$(3)$ Both $\vec{B}$ and $\vec{E}$ are mutually perpendicular and perpendicular to the direction of velocity.
$(4)$ $\vec{B}$ should be along the direction of velocity and $\vec{E}$ should be perpendicular to the direction of velocity.
Which one of the following pairs of statements is possible?

$A$ particle of mass $m = 1.67 \times 10^{-27} \, kg$ and charge $q = 1.6 \times 10^{-19} \, C$ enters a region of uniform magnetic field of strength $B = 1 \, T$ as shown in the figure. The angle of incidence is $45^{\circ}$. The radius of the circular portion of the path is:

An electron is projected normally from the surface of a sphere of radius $a$ with speed $v_0$ into a uniform magnetic field $B$ perpendicular to the plane of the paper. The centre of the sphere is at a distance $b$ from a wall. If the electron strikes the wall tangentially,what should be the magnetic field $B$?

Two particles $X$ and $Y$ having equal charges,after being accelerated through the same potential difference,enter a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The ratio of the mass of $X$ to that of $Y$ is