$A$ body is projected vertically from the surface of the earth of radius $R$ with a velocity equal to half of the escape velocity. The maximum height reached by the body is

If $\vec F$ is the force acting on a particle having position vector $\vec r$ and $\vec \tau$ is the torque of this force about the origin,then:

What type of polymer is natural rubber?

Consider the general reaction given below at $400 \ K$: $xA_{(g)} \rightleftharpoons yB_{(g)}$. The values of $K_p$ and $K_c$ are studied under the same condition of temperature but variation in $x$ and $y$. $(i)$ $K_p = 85.87$ and $K_c = 2.586$ (appropriate units). $(ii)$ $K_p = 0.862$ and $K_c = 28.62$ (appropriate units). The values of $x$ and $y$ in $(i)$ and $(ii)$ respectively are:

The number of possible enantiomeric pairs that can be produced on monochlorination of $2$-methylbutane is

$A$ narrow parallel beam of light is incident paraxially on a solid transparent sphere of radius $r$ kept in air. What should be the refractive index if the beam is to be focused at the farther surface of the sphere?