$A$ square of side $3\;cm$ is placed at a distance of $25\;cm$ from a concave mirror of focal length $10\;cm$. The centre of the square is at the axis of the mirror and the plane is normal to the axis. The area enclosed by the image of the square is $......\;cm^2$.

Which of the following statements is true?

$A$ magnetic needle lying parallel to a magnetic field is turned through $60^{\circ}$. The work done on it is $W$. The torque required to maintain the magnetic needle in the position mentioned above is

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$,where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = [U(x = \infty) - U_{\text{equilibrium}}]$,what is the value of $D$?

In a resonance pipe,the first and second resonances are obtained at lengths $22.7 \ cm$ and $70.2 \ cm$ respectively. What will be the end correction in $cm$?

The force constant of a wire is $k$ and that of another wire is $2k$. When both the wires are stretched through the same distance,then the work done is: