The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m, l$ and $d$ are $97.42 \pm 0.02 \mathrm{~g}$, $8.35 \pm 0.05 \mathrm{~mm}$ and $20.20 \pm 0.02 \mathrm{~mm}$, respectively. Calculated percentage fractional error in $\rho$ is $\_\_\_\_$ .
The potential energy of a particle changes with distance $x$ from a fixed origin as $V=\frac{A \sqrt{x}}{x+B}$, where $A$ and $B$ are constant with appropriate dimensions. The dimensions of $A B$ are $\_\_\_\_$
$$ \text { Match List - I with List - II. } $$
| $$ \text { List - I } $$ |
$$ \text { List - II } $$ |
||
|---|---|---|---|
| A. | Meter (L) | I. | $$ \sqrt{\frac{h c}{G}} $$ |
| B. | Second (S) | II. | $$ \sqrt{\frac{G h}{c^5}} $$ |
| C. | Kilogram (M) | III. | $$ \sqrt{\frac{K^2 L^2 c^3}{G h}} $$ |
| D. | Kelvin (K) | IV. | $$ \sqrt{\frac{G h}{c^3}} $$ |
where h (Planck's constant), G (gravitational constant) and c (speed of light in vacuum) as fundamental units.
Choose the correct answer from the options given below :
In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A , respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA , respectively. The estimated error in the resistance measurement is $\_\_\_\_$ $\Omega$
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