The force required to stretch a steel wire of area of cross-section $1 \mathrm{~mm}^2$ to double its length is

(Young's modulus of steel $=2 \times 10^{11} \mathrm{~N}-\mathrm{m}^{-2}$ )

When a wire of length ' $L$ ' clamped at one end is pulled by a force ' $F$ ' from the other end, its length increases by ' $L$ '. If the radius of the wire and the applied force were halved, then the increase in its length is

When a sphere is taken to the bottom of a sea of depth 1 km , it contracts in volume by $0.01 \%$, then the Bulk modulus of the material of the sphere is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

As shown in the figure, a light uniform rod $P Q$ of length 150 cm is suspended from the ceiling horizontally using two metal wires $A$ and $B$ tied to the ends of the rod. The ratios of the radii and the Young's moduli of the materials of the two wires $A$ and $B$ are respectively $2: 3$ and $3: 2$. The position at which a weight should be suspended from the rod such that the elongations of the two wires become equal is