But $\frac{1}{2} m v^{2}=e V$ or $v=\sqrt{\frac{2 e V}{m}}$
$\therefore F=B q \sqrt{\frac{2e v}{m}}$
$\Rightarrow F \propto \sqrt{V}$ and
$F \propto \sqrt{2 V}$
$\frac{F^{\prime}}{F}=\sqrt{2}$ or $F^{\prime}=\sqrt{2} F$
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| Column $I$ | Column $II$ |
| $(A)$ An insulated container has two chambers separated by a valve. Chamber $I$ contains an ideal gas and the Chamber $II$ has vacuum. The valve is opened. | $(p)$ The temperature of the gas decreases |
| $(B)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $\mathrm{P} \propto \frac{1}{\mathrm{~V}^2}$, where $\mathrm{V}$ is the volume of the gas | $(q)$ The temperature of the gas increases or remains constant |
| $(C)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $\mathrm{P} \propto \frac{1}{\mathrm{~V}^{4 / 3}}$, where $\mathrm{V}$ is its volume | $(r)$ The gas loses heat |
| $(D)$ An ideal monoatomic gas expands such that its pressure $\mathrm{P}$ and volume $\mathrm{V}$ follows the behaviour shown in the graph $Image$ | $(s)$ The gas gains heat |
$1.$ What is the maximum energy of the anti-neutrino?
$(A)$ Zero
$(B)$ Much less than $0.8 \times 10^6 \ eV$
$(C)$ Nearly $0.8 \times 10^6 \ eV$
$(D)$ Much larger than $0.8 \times 10^6 \ eV$
$2.$ If the anti-neutrino had a mass of $3 eV / c ^2$ (where $c$ is the speed of light) instead of zero mass, what should be the range of the kinetic energy, $K$, of the electron?
$(A)$ $0 \leq K \leq 0.8 \times 10^6 \ eV$
$(B)$ $3.0 eV \leq K \leq 0.8 \times 10^6 \ eV$
$(C)$ $3.0 eV \leq K < 0.8 \times 10^6 \ eV$
$(D)$ $0 \leq K < 0.8 \times 10^6 \ eV$
Give the answer question $1$ and $2.$
