$A$ block of mass $0.50 \ kg$ is moving with a speed of $2.00 \ ms^{-1}$ on a smooth surface. It strikes another mass of $1.00 \ kg$ (initially at rest) and then they move together as a single body. The energy loss during the collision is .............. $J$

$A$ container is filled with water $(\mu = 1.33 \approx 4/3)$ up to a height of $33.25 \, cm$. $A$ concave mirror is placed $15 \, cm$ above the water level. The image of an object placed at the bottom is formed by the mirror at $25 \, cm$ below the water level. The focal length of the mirror is: (in $, cm$)

In a co-axial,straight cable,the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero:

Two nuclei have their mass numbers in the ratio of $1 : 3.$ The ratio of their nuclear densities would be

The area (in square units) of the region enclosed by the two circles $x^2+y^2=1$ and $(x-1)^2+y^2=1$ is

An electron moving with a speed $u$ along the positive $x-$ axis at $y = 0$ enters a region of uniform magnetic field $\vec{B} = -B_0\hat{k}$ which exists to the right of the $y-$ axis. The electron exits from the region after some time with the speed $v$ at coordinate $y$. Then: