Which of the following physical quantities has a unit but no dimensions ?
A
Relative velocity
B
Relative density
C
Strain
D
Angle
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D
Angle
d Among the given physical quantities angle has a unit but no dimensions. Angle $ = \left[ {{M^0}{L^0}{T^0}} \right]$ The $SI\, unit$ of angle is radian
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The temperature of two bodies measured by a thermometer are $t_1 = 20\, ^oC + 0.5\, ^oC$ and $t_2 = 50\,^oC + 0.5\, ^oC$. The temperature difference and the error there in is
The period of oscillation of a simple pendulum is given by $T = 2\pi \sqrt {\frac{l}{g}} $ where $l$ is about $100 \,cm$ and is known to have $1\,mm$ accuracy. The period is about $2\,s$. The time of $100$ oscillations is measured by a stop watch of least count $0.1\, s$. The percentage error in $g$ is ......... $\%$
A student performs an experiment to determine the Young's modulus of a wire, exactly $2 \mathrm{~m}$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 \mathrm{~mm}$ with an uncertainty of $\pm 0.05 \mathrm{~mm}$ at a load of exactly $1.0 \mathrm{~kg}$. The student also measures the diameter of the wire to be $0.4 \mathrm{~mm}$ with an uncertainty of $\pm 0.01 \mathrm{~mm}$. Take $g=9.8 \mathrm{~m} / \mathrm{s}^2$ (exact). The Young's modulus obtained from the reading is
What is the dimensional formula of $a b^{-1}$ in the equation $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where letters have their usual meaning.
What is the fractional error in $g$ calculated from $T = 2\pi \sqrt {l/g} $ ? Given fraction errors in $T$ and $l$ are $ \pm x$ and $ \pm y$ respectively?
Measure of two quantities along with the precision of respective measuring instrument $A = 2.5\,m{s^{ - 1}} \pm 0.5\,m{s^{ - 1}}$, $B = 0.10\,s \pm 0.01\,s$ The value of $AB$ will be