Two small spherical balls of mass 10 g each with charges $-2 \mu \mathrm{C}$ and $2 \mu \mathrm{C}$, are attached to two ends of very light rigid rod of length 20 cm . The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of $100 \mu \mathrm{C} / \mathrm{m}^2$ such that length of rod makes an angle of $30^{\circ}$ with electric field generated by charge sheet. Net torque acting on the rod is: (Take $\varepsilon_{\mathrm{o}}: 8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$ )

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $\sqrt{\frac{x}{5}}$ where $x=$ ________.

Distance between object and its image (magnified by $-\frac{1}{3}$ ) is 30 cm . The focal length of the mirror used is $\left(\frac{x}{4}\right) \mathrm{cm}$, where magnitude of value of $x$ is _________.

Two slabs with square cross section of different materials $(1,2)$ with equal sides $(l)$ and thickness $d_1$ and $d_2$ such that $d_2=2 d_1$ and $l>d_2$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is $\theta_2=2 \theta_1$. If the shear moduli of material 1 is $4 \times 10^9 \mathrm{~N} / \mathrm{m}^2$, then shear moduli of material 2 is $x \times 10^9 \mathrm{~N} / \mathrm{m}^2$, where value of $x$ is ________.