In order to shift a body of mass $m$ from a circular orbit of radius $3R$ to a higher radius $5R$ around the earth,the work done is

$A$ segment of wire vibrates with a fundamental frequency of $450 ~Hz$ under a tension of $9 ~kg-wt$. The tension at which the fundamental frequency of the same wire becomes $900 ~Hz$ is

The equivalent resistance of a series combination of two resistors is $s$. When they are connected in parallel,the equivalent resistance is $p$. If $s = np$,then the minimum value for $n$ is (Round off to the nearest integer).

Bromine is commercially prepared from sea water by displacement reaction:
$Cl_2 + 2Br^{-}_{(aq)} \to 2Cl^{-}_{(aq)} + Br_2$
$Br_2$ gas thus formed is dissolved into a solution of $Na_2CO_3$ and then pure $Br_2$ is obtained by treatment of the solution with:

$A$ bimetallic strip consists of metals $X$ and $Y$. It is mounted rigidly at the base as shown in the figure. The metal $X$ has a higher coefficient of linear expansion compared to that of metal $Y$. When the bimetallic strip is placed in a cold bath, what happens?

The area (in sq. units) of the triangle formed by the tangent and the normal at the point $\left(\frac{a}{\sqrt{2}}, \frac{b}{\sqrt{2}}\right)$ to the curve $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and the $X$-axis is