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The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right)\,(V - b) = RT$. Here $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature and $a,\,b,\,R$ are constants. The dimensions of $'a'$ are
The quantities $\quad x=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}, y=\frac{E}{B}$ and $z=\frac{l}{C R}$ are defined where $C-$ capacitance $R-$Resistance, $l-$length, $E-$Electric field, $B-$magnetic field and $\varepsilon_{0}, \mu_{0},$ -free space permittivity and permeability respectively. Then....
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 length of a uniform rod is $100.0 \,cm$ and radius is $1.00 \,cm$. If length is measured with a meter rod having least count $1 \,mm$ and radius is measured with vernier callipers having least count $0.1 \,mm$, the percentage error in calculated volume of cylinder is ............. $\%$