If $Q= \frac{X^n}{Y^m}$ and $\Delta X$ is absolute error in the measurement of $X,$ $\Delta Y$ is absolute error in the measurement of $Y,$ then absolute error $\Delta Q$ in $Q$ is
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
A sliver wire has mass $(0.6 \pm 0.006) \; g$, radius $(0.5 \pm 0.005) \; mm$ and length $(4 \pm 0.04) \; cm$. The maximum percentage error in the measurement of its density will be $......\,\%$
A dimensionless quantity is constructed in terms of electronic charge $e$, permittivity of free space $\varepsilon_0$, Planck's constant $h$, and speed of light $c$. If the dimensionless quantity is written as $e^\alpha \varepsilon_0^\beta h^7 c^5$ and $n$ is a non-zero integer, then $(\alpha, \beta, \gamma, \delta)$ is given by
The equation of state of a real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where $\mathrm{P}, \mathrm{V}$ and $\mathrm{T}$ are pressure. volume and temperature respectively and $R$ is the universal gas constant. The dimensions of $\frac{a}{b^2}$ is similar to that of :
Diameter of a steel ball is measured using a Vernier callipers which has divisions of $0. 1\ cm$ on its main scale $(MS)$ and $10$ divisions of its vernier scale $(VS)$ match $9$ divisions on the main scale. Three such measurements for a ball are given as
S.No.
$MS\ (cm)$
$VS$ divisions
$(1)$
$0.5$
$8$
$(2)$
$0.5$
$4$
$(3)$
$0.5$
$6$
If the zero error is $- 0.03\ cm,$ then mean corrected diameter is $........... cm$
If $x$ and $a$ stand for distance then for what value of $n$ is given equation dimensionally correct the eq. is $\int {\frac{{dx}}{{\sqrt {{a^2}\, - \,{x^n}} \,}}\, = \,{{\sin }^{ - 1}}\,\frac{x}{a}} $
From the following combinations of physical constants $($expressed through their usual symbols$)$ the only combination, that would have the same value in different systems of units, is