The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at $V_z=5 \mathrm{~V}$ and the desired current in load is 5 mA . The unregulated voltage source can supply upto 25 V . Considering the Zener diode can withstand four times of the load current, the value of resistor $R_s$ (shown in circuit) should be $\_\_\_\_$ $\Omega$.

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$ through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire when it travells a vertical distance of 200 m is $\_\_\_\_$ mV .

$$ \text { Match List - I with List - II. } $$

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Two small balls with masses $m$ and 2 m are attached to both ends of a rigid rod of length $d$ and negligible mass. If angular momentum of this system is $L$ about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about $A$ is :