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Physics · UNITS AND MEASUREMENT
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Physics · UNITS AND MEASUREMENT
A spherical surface area element \( dA = 0.25\text{ m}^2 \) at a distance \( r = 0.5\text{ m} \) from the center subtends a solid angle \( \Omega \). An arc of length \( ds = 0.2\text{ m} \) on a circle of the same radius \( r = 0.5\text{ m} \) subtends a plane angle \( \theta \). The ratio of the numerical value of \( \Omega \) (in steradians) to \( \theta \) (in radians) is:
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As illustrated in Fig. 1.1(b), a solid angle \( d\Omega \) is defined as the ratio of intercepted area \( dA \) of a spherical surface to the square of its radius \( r^2 \). A flat circular disc of radius \( R \) is placed perpendicular to the axis at a distance \( d = \sqrt{3}R \) from an apex \( O \). The solid angle subtended by the disc at the apex \( O \) is:
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A substance of mass \( 5.74\text{ g} \) occupies a volume of \( 1.2\text{ cm}^3 \). Keeping the significant figures in view, its density should be expressed as:
Read answer →Physics · UNITS AND MEASUREMENT
One mole of an ideal gas at STP occupies \( 22.4\text{ L} \). Taking the size of a hydrogen molecule to be about \( 1\text{ \AA} \), what is the ratio of molar volume to the atomic volume of a mole of hydrogen molecules?
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What is the number of significant figures in each of the measured lengths \( l = 16.2 \text{ cm} \) and \( b = 10.1 \text{ cm} \)?
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The force \( F \) acting on an object as a function of position \( x \) and time \( t \) is given by \( F = A \sqrt{x} + B t^2 + C \ln(D x) \). The dimensional formula of \( \frac{A \cdot B}{D} \) is:
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What is the number of significant figures in the measured length \( 23080\text{ }\mu\text{m} \)?
Read answer →Physics · UNITS AND MEASUREMENT
Evaluate the sum \( 436.32 \text{ g} + 227.2 \text{ g} + 0.301 \text{ g} \) by properly considering the rules of significant figures and decimal places in addition.
Read answer →Physics · UNITS AND MEASUREMENT
Velocity \( v \) of a wave on a stretched string depends on tension \( F \) and mass per unit length \( \mu \). The correct relation between \( v \), \( F \), and \( \mu \) obtained by dimensional analysis is:
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The mean length of a rod measured by Vernier callipers is to be reported. Why is a set of 100 measurements expected to yield a more reliable estimate than a set of 5 measurements?
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Which of the following equations is dimensionally INCORRECT? (where \( s \) is displacement, \( u \) is initial velocity, \( a \) is acceleration, \( t \) is time, \( \lambda \) is wavelength, and \( T \) is time period)
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What determines the precision of a measurement reflected by the number of significant figures?
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Consider the following measured values: (i) \( 0.002030\text{ m} \), (ii) \( 2.030 \times 10^3\text{ m} \), (iii) \( 2030\text{ m} \). The number of significant figures in (i), (ii), and (iii) respectively are:
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If the length \( l = 16.2 \pm 0.1 \text{ cm} \), what is the percentage error in the measurement of length \( l \)?
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How many significant figures do the exact numbers appearing in formulae like \( 2\pi \) in \( T = 2\pi\sqrt{\frac{L}{g}} \) have?
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The van der Waals equation for a real gas is given by \( (P + \frac{a}{V^2})(V - b) = RT \), where \( P \) is pressure, \( V \) is volume, and \( T \) is temperature. The dimensional formula for the ratio \( \frac{a}{b^2} \) is:
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A rectangular metal sheet has a length of \( 4.234 \text{ m} \), a breadth of \( 1.005 \text{ m} \), and a thickness of \( 2.01 \text{ cm} \). The total surface area of the sheet reported to appropriate significant figures is:
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Which of the following physical quantities have equivalent dimensions in mechanics?
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When looking out of the window of a fast-moving train, nearby objects appear to move rapidly in the opposite direction while distant objects (like hill tops and the Moon) appear stationary. This phenomenon illustrates the concept of:
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What is the term for a complete set of units, comprising both base units and derived units?
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What is the full form of the internationally accepted system of units abbreviated as SI?
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In the measurement of the period of oscillation of a simple pendulum given as \( 1.62 \text{ s} \), which of the following statements is correct regarding its digits?
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