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PHYSICAL WORLD AND MEASUREMENT
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PHYSICAL WORLD AND MEASUREMENT
Very Short Answer Questions
Q2. What is Raman effect?
Q3. What is Chandrasekhar Limit?
Q4. State the fundamental forces in nature.
Q5. Define accuracy and precision.
Q6. How can you minimise systematic errors?
Q7. Express one a.m.u. in kg.
Q8. Define significant figures. Why are they important in measurements?
Q9. State the rules for determining the number of significant figures in a measured quantity.
Q10. What do you mean by dimensional formula? Give the dimensional formula of force.
Q11. How are SI base units different from derived units? Give one example of each.
Q12. What do you mean by the term 'order of magnitude'? Give an example.
Q13. Write the dimensional equation of kinetic energy. Use it to check the dimensional consistency of the formula.
Q14. Write the dimensional equation of kinetic energy. Use it to check the dimensional consistency of the formula \(K=\frac{1}{2}mv^2\).
Q15. State the principle of homogeneity of dimensions. How is it used to check the correctness of an equation?
Q16. What is the difference between a fundamental unit and a derived unit? Give two examples each.
Q17. Express \(1\) angstrom in terms of metres. Also, express \(0.5\,\mathrm{\AA}\) in scientific notation.
Q1. What is meant by dimensional analysis? Give one application.
Q2. The length and breadth of a rectangle are measured as 16.2 cm and 10.1 cm respectively. Find the percentage error in the area.
Q3. A student reports the density of a substance as 4.8 g/cm³ from measurements with values 5.74 g and 1.2 cm³. Justify the number of significant figures used.
Q4. State the SI base unit of temperature. How is it defined currently?
Q5. Using dimensional analysis, deduce the relation for the time period of a simple pendulum assuming it depends on length and acceleration due to gravity.
Q1. Explain the nature and scope of physics and its relation with technology and society.
Q2. Explain the measurement of physical quantities, systems of units, errors in measurement and significant figures.
Q3. Explain dimensional analysis, its applications and limitations.
Q1. In the equation P = E¹ M² G?², the quantities E, M and G denote energy, angular momentum, mass and gravitational constant respectively. Show that P is a dimensionless quantity.
Q2. If the velocity of light c, Planck's constant h and the gravitational constant G are taken as fundamental quantities, express length and time in terms of these quantities.
Q3. An artificial satellite is revolving around a planet of mass M and radius R in a circular orbit of radius r. Show that the time period is proportional to r^(3/2)/sqrt(GM).
Q4. State the number of significant figures in the following: 6729, 0.0024, 0.08240, 6.032, 4.57 × 10?¹?.
Q5. A stick has a length of 12.132 cm and another has a length of 12.4 cm. If the two sticks are placed end to end, find the total length and the difference in their lengths.
Q6. Each side of a cube is measured as 7.203 cm. What is the total surface area and the volume of the cube, to appropriate significant figures?
Q7. A body of mass 2.42 g and volume 4.7 cm³ is measured with possible errors of 0.1 g and 0.1 cm³. Find the error in density.
Q8. The error in measurement of radius of a sphere is 1%. What is the error in its area?
Q9. The percentage error in mass and speed are 2% and 3% respectively. Find the maximum percentage error in kinetic energy calculated using these quantities.
Q10. One mole of an ideal gas at standard temperature and pressure occupies 22.4 L volume. If the size of the hydrogen molecule is assumed negligible, find the ratio of molar volume to atomic volume.
Q1. Each side of a cube is measured to be \(7.203\,\mathrm{m}\). What are the total surface area and the volume of the cube to appropriate significant figures?
Q2. \(5.74\,\mathrm{g}\) of a substance occupies \(1.2\,\mathrm{cm^3}\). Express its density by keeping the significant figures in view.
Q3. Let us consider an equation \(\frac{1}{2}mv^2=mgh\), where \(m\) is the mass of the body, \(v\) its velocity, \(g\) is the acceleration due to gravity and \(h\) is the height. Check whether this equation is dimensionally correct.
Q4. The SI unit of energy is \(J=\mathrm{kg\,m^2\,s^{-2}}\); that of speed \(v\) is \(\mathrm{m\,s^{-1}}\) and of acceleration \(a\) is \(\mathrm{m\,s^{-2}}\). Which of the formulae for kinetic energy \(K\) given below can you rule out on the basis of dimensional arguments (m stands for the mass of the body): (a) \(K=m^2v^3\) (b) \(K=\frac{1}{2}mv^2\) (c) \(K=ma\) (d) \(K=\frac{3}{16}mv^2\) (e) \(K=\frac{1}{2}mv^2+ma\)?
Q5. Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length \(l\), mass of the bob \(m\) and acceleration due to gravity \(g\). Derive the expression for its time period using method of dimensions.
Q6. Find the relative error in \(Z\) if \(Z=\frac{AB^2}{CD}\).
Q7. The period of oscillation of a simple pendulum is \(T=2\pi\sqrt{\frac{L}{g}}\). Measured value of \(L\) is \(20.0\,\mathrm{cm}\), known to \(1\,\mathrm{mm}\) accuracy and time for \(100\) oscillations of the pendulum is found to be \(90\,\mathrm{s}\) using a stop watch of \(1\,\mathrm{s}\) resolution. What is the accuracy in the determination of \(g\)?
Q8. Each side of a cube is measured to be \(7.203\,\mathrm{m}\). What are the total surface area and the volume of the cube to appropriate significant figures?
Q9. \(5.74\,\mathrm{g}\) of a substance occupies \(1.2\,\mathrm{cm^3}\). Express its density by keeping the significant figures in view.
Q10. Let us consider an equation \(\frac{1}{2}mv^2=mgh\), where \(m\) is the mass of the body, \(v\) its velocity, \(g\) is the acceleration due to gravity and \(h\) is the height. Check whether this equation is dimensionally correct.
Q11. The SI unit of energy is \(J=\mathrm{kg\,m^2\,s^{-2}}\); that of speed \(v\) is \(\mathrm{m\,s^{-1}}\) and of acceleration \(a\) is \(\mathrm{m\,s^{-2}}\). Which of the formulae for kinetic energy \(K\) given below can you rule out on the basis of dimensional arguments (m stands for the mass of the body): (a) \(K=m^2v^3\) (b) \(K=\frac{1}{2}mv^2\) (c) \(K=ma\) (d) \(K=\frac{3}{16}mv^2\) (e) \(K=\frac{1}{2}mv^2+ma\)?
Q12. Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length \(l\), mass of the bob \(m\) and acceleration due to gravity \(g\). Derive the expression for its time period using method of dimensions.