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Physics · UNITS AND MEASUREMENT
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Physics · UNITS AND MEASUREMENT
A vehicle moving with a speed of \( 18\text{ km h}^{-1} \) covers how many meters in \( 1\text{ s} \)?
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Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard known as:
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Which of the following measurements has the highest relative error?
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The length of three rods are measured as \( 15.24\text{ cm} \), \( 0.082\text{ cm} \), and \( 1.3\text{ cm} \). Their total length, expressed with due regard to significant figures, is:
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In Einstein's mass-speed relation, a student correctly writes \( m = \frac{m_0}{(1 - v^2/x)^{1/2}} \) but forgets the position of speed of light \( c \). By dimensional analysis, the correct form of \( x \) must be:
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What is the dimensional equation for force \( F \)?
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Which of the following is a fundamental (base) physical quantity according to the International System of Units (SI)?
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The unit of length convenient on the atomic scale is known as an angstrom (\( \text{\AA} \)). Given that \( 1\text{ \AA} = 10^{-10}\text{ m} \), what is the total atomic volume in \( \text{m}^3 \) of a mole of hydrogen atoms if the size of a hydrogen atom is about \( 0.5\text{ \AA} \)?
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According to the rules for arithmetic operations with significant figures, if the mass of an object is \( 4.237 \text{ g} \) and its volume is \( 2.51 \text{ cm}^3 \), the density reported should be to how many significant figures?
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Refer to the diagram shown below from page 2 of the textbook. A plane angle \( d\theta \) is defined as \( d\theta = \frac{ds}{r} \) and a solid angle \( d\Omega \) as \( d\Omega = \frac{dA}{r^2} \). If a spherical surface of radius \( r = 2.0\text{ m} \) has a cap of surface area \( dA = 0.8\text{ m}^2 \), what is the solid angle subtended by this cap at the center of the sphere?
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In the revised SI system (2018), the base unit 'ampere' is defined by fixing the numerical value of elementary charge \( e \) to be \( 1.602176634 \times 10^{-19} \) when expressed in C (or A s). If a current of \( 1.6\text{ A} \) flows through a conductor for \( 10\text{ seconds} \), the total number of electrons passing through any cross-section is closest to:
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Units of all other physical quantities that can be expressed as combinations of the base units are called:
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If the length and breadth of a rectangular sheet are measured as \( l = 16.2\text{ cm} \) and \( b = 10.1\text{ cm} \), the percentage error in area and absolute error in area respectively are:
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If Planck's constant (\( h \)), speed of light in vacuum (\( c \)), and Newton's gravitational constant (\( G \)) are taken as fundamental quantities, the dimension of time in terms of \( h \), \( c \), and \( G \) is:
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The length and breadth of a rectangular field are measured as \( l = (20.0 \pm 0.2)\text{ m} \) and \( b = (10.0 \pm 0.1)\text{ m} \). The percentage uncertainty in the calculated area of the field is:
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Which of the following was NOT one of the traditional systems of units used extensively before the universal adoption of the SI system?
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In a physical calculation, pressure \( P \) varies with distance \( z \) according to the relation \( P = \frac{\alpha}{\beta} e^{-\frac{\alpha z}{k_B T}} \), where \( k_B \) is Boltzmann's constant and \( T \) is absolute temperature. The dimensional formula of \( \beta \) is:
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The dimensional formula of the ratio of Planck's constant \( h \) to Boltzmann's constant \( k_B \) is:
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The speed of sound \( v \) in a gas depends on the pressure \( P \) and density \( \rho \) of the gas as \( v = k P^x \rho^y \), where \( k \) is a dimensionless constant. The values of exponents \( x \) and \( y \) are:
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When rounding off numbers according to standard conventions, if the insignificant digit to be dropped is 5, and the preceding digit is even, then:
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The resistance \( R = \frac{V}{I} \) where \( V = (100 \pm 5)\text{ V} \) and \( I = (10 \pm 0.2)\text{ A} \). The total percentage error in \( R \) is:
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Consider the measured values: (i) \( 0.002308\text{ m} \), (ii) \( 2.3080\text{ m} \), (iii) \( 23080\text{ m} \), and (iv) \( 2.308 \times 10^3\text{ m} \). The number of significant figures in these measurements are respectively:
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