The percentage error in the calculated volume of a sphere, if there is $2 \%$ error in its diameter measurement, is $\_\_\_\_$ .
$$ \text { Match List - I with List - II. } $$
| $$ \text { List - I } $$ |
$$ \text { List - II } $$ |
||
|---|---|---|---|
| A. | Boltzmann constant | I. | $$ \left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right] $$ |
| B. | Stefan's constant | II. | $$ \left[\mathrm{M} \mathrm{~L}^2 \mathrm{~T}^{-1}\right] $$ |
| C. | Planck's constant | III. | $$ \left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right] $$ |
| D. | Gravitational constant | IV. | $$ \left[\mathrm{M} \mathrm{~L}^0 \mathrm{~T}^{-3} \mathrm{~K}^{-4}\right] $$ |
Choose the correct answer from the options given below :
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 $\_\_\_\_$
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