Two particles $A$ and $B$,initially at rest,move towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the center of mass of the system is:

$A$ conducting circular loop is placed in a uniform magnetic field,$B = 0.025 \, T$,with its plane perpendicular to the magnetic field. The radius of the loop is made to shrink at a constant rate of $1 \, mm/s$. The induced $e.m.f.$ when the radius is $2 \, cm$ is

Which of the following compounds is soluble in benzene but almost insoluble in water?

The correct statement$(s)$ regarding defects in solids is/are:

The shadow of a tower standing on a level ground is found to be $60 \, m$ longer when the sun's altitude is $30^\circ$ than when it is $45^\circ$. The height of the tower is

An inductance of $\frac{200}{\pi} \ mH$,a capacitance of $\frac{10^{-3}}{\pi} \ F$ and a resistance of $10 \ \Omega$ are connected in series with an $AC$ source of $220 \ V, 50 \ Hz$. The phase angle of the circuit is: