For a telescope,the focal length of the objective lens is $15 \ cm$ and the focal length of the eyepiece is $10 \ mm$. If the tube length is $16 \ cm$,find the magnification.

During an adiabatic process,the pressure of a gas is proportional to the cube of its temperature. The value of $C_p / C_V$ for that gas is

$A$ disc of mass $M$ and radius $R$ is rolling with angular speed $\omega$ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin $O$ is

$A$ meter bridge is set up as shown,to determine an unknown resistance '$X$' using a standard $10 \, \Omega$ resistor. The galvanometer shows a null point when the tapping-key is at the $52 \, cm$ mark. The end corrections are $1 \, cm$ and $2 \, cm$ respectively for the ends $A$ and $B$. The determined value of '$X$' is $.......... \Omega$.

As shown in the figure,charges $+q$ and $-q$ are placed at the vertices $B$ and $C$ of an isosceles triangle. The potential at the vertex $A$ is

If the gravitational acceleration at the surface of the Earth is $g$,then the increase in potential energy in lifting an object of mass $m$ to a height equal to half of the radius of the Earth from the surface will be: