**Question:**

A galvanometer of resistance $100 \Omega$ has 50 divisions on its scale and has sensitivity of $20 \mu \mathrm{A} /$ division. It is to be converted to a voltmeter with three ranges, of $0-2 \mathrm{~V}, 0-10$ $\mathrm{V}$ and $0-20 \mathrm{~V}$. The appropriate circuit to do so is :

Correct Option: 3

**Solution:**

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An electron is moving along $+x$ direction with a velocity of $6 \times 10^{6} \mathrm{~ms}^{-1}$. It enters a region of uniform electric field of $300 \mathrm{~V} / \mathrm{cm}$ pointing along $+y$ direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the $x$ direction will be:

A particle of charge $q$ and mass $m$ is moving with a velocity $-v \hat{i}(v \neq 0)$ towards a large screen placed in the $\mathrm{Y}-\mathrm{Z}$ plane at a distance $d$. If there is a magnetic field $\vec{B}=B_{0} \hat{k}$, the minimum value of $v$ for which the particle will not hit the screen is:

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The figure shows a region of length ‘ $l$ ‘ with a uniform magnetic field of $0.3 \mathrm{~T}$ in it and a proton entering the region with velocity $4 \times 10^{5} \mathrm{~ms}^{-1}$ making an angle $60^{\circ}$ with the field. If the proton completes 10 revolution by the time it cross the region shown, ‘ $l$ ‘ is close to (mass of proton $=1.67 \times 10^{-27} \mathrm{~kg}$, charge of the proton $=1.6 \times 10^{-19} \mathrm{C}$ )

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