A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T . If the resistance of the total circuit is $2 \Omega$ then the force needed to move the rod towards right with constant speed $(v)$ of $1.5 \mathrm{~m} / \mathrm{s}$ is $\_\_\_\_$ N.

10 mole of oxygen is heated at constant volume from $30^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. The change in the internal energy of the gas is $\_\_\_\_$ cal. (The molecular specific heat of oxygen at constant pressure, $C_P=7 \mathrm{cal} / \mathrm{mol} .{ }^{\circ} \mathrm{C}$ and $\left.\mathrm{R}=2 \mathrm{cal} . / \mathrm{mol} .{ }^{\circ} \mathrm{C}.\right)$

In a microscope the objective is having focal length $f_o=2 \mathrm{~cm}$ and eye-piece is having focal length $f_e=4 \mathrm{~cm}$. The tube length is 32 cm . The magnification produced by this microscope for normal adjustment is $\_\_\_\_$ .

Two identical thin rods of mass $M \mathrm{~kg}$ and length $L \mathrm{~m}$ are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point $P$ and perpendicular to the plane of the rods is $\frac{x}{12} \mathrm{ML}^2 \mathrm{~kg} \mathrm{~m}^2$. The value of $x$ is $\_\_\_\_$ .