The correct order of the $O-O$ bond length in $O_2, H_2O_2$,and $O_3$ is

$A$ circular disc of radius $R$ is removed from a bigger uniform circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

In the equation $\log\, S = \log\, C + Z\, \log\, A$,what does $S$ represent?

An ideal gas of mass $m$ in a state $A$ goes to another state $B$ via three different processes as shown in the figure. If ${Q_1}, {Q_2}$ and ${Q_3}$ denote the heat absorbed by the gas along the three paths,then

$A$ pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2+y^2=4$ with $x+y=a$. The set containing the value of $a$ is

As shown in the figure,two particles each of mass $m$ tied at the ends of a light string of length $2 a$ are kept on a frictionless horizontal surface. When the mid-point $(P)$ of the string is pulled vertically upwards with a small but constant force $F$,the particles move towards each other on the surface. The magnitude of acceleration of each particle,when the separation between them becomes $2 x$,is: