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The dimensional formula for a physical quantity $x$ is $\left[ M ^{-1} L ^{3} T ^{-2}\right]$. The errors in measuring the quantities $M , L$ and $T$ respectively are $2 \%, 3 \%$ and $4 \%$. The maximum percentage of error that occurs in measuring the quantity $x$ is
If the velocity of light $c$, universal gravitational constant $G$ and planck's constant $h$ are chosen as fundamental quantities. The dimensions of mass in the new system is
In an experiment four quantities $a, b, c$ and $d$ are measured with percentage error $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $w$ is calculated as follows $w\, = \,\frac{{{a^4}{b^3}}}{{{c^2}\sqrt D }}$ error in the measurement of $w$ is .......... $\%$
The force of interaction between two atoms is given by $F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);$ where $x$ is the distance, $k$ is the Boltzmann constant and $T$ is temperature and $\alpha $ and $\beta $ are two constants. The dimension of $\beta $ is
Students $A, B$ and $C$ measure the length of a room using $25 \,m$ long measuring tape of least count $0.5 \,cm$, meter-scale of least count $0.1 \,cm$ and a foot-scale of least count $0.05 \,cm$, respectively. If the specified length of the room is $9.5 \,m$, then which of the following students will report the lowest relative error in the measured length?
The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are $4\%$ and $3\%$ respectively, the maximum error in the measurement of density will be ........ $\%$