The radius $R$ of the soap bubble is doubled under isothermal conditions. If $T$ is the surface tension of the soap bubble,the work done in doing so is given by: (in $\pi R^{2} T$)

$A$ lead bullet of mass $10 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of heat is absorbed by the bullet,the increase in its temperature is (Specific heat of lead $= 150 \ J/kg \cdot ^{\circ}C$) (in $^{\circ}C$)

Three rings,each having equal radius $R$,are placed mutually perpendicular to each other and each having its centre at the origin of the coordinate system. If current $I$ is flowing through each ring,then the magnitude of the magnetic field at the common centre is

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300\ K.$ The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30\ K,$ then the rise in temperature of the gas in $B$ is ....... $K$

$A$ bullet of mass $10\,g$ moving horizontally with a velocity of $400\,m/s$ strikes a wooden block of mass $2\,kg$ which is suspended by a light inextensible string of length $5\,m$. As a result,the centre of gravity of the block is found to rise a vertical distance of $10\,cm$. The speed of the bullet after it emerges out horizontally from the block will be ............... $m/s$.

Observe the following reaction: $2A + B \longrightarrow C$. The rate of formation of $C$ is $2.2 \times 10^{-3} \ mol \ L^{-1} \ min^{-1}$. What is the value of $-\frac{d[A]}{dt}$ (in $mol \ L^{-1} \ min^{-1}$)?