101. For a sphere having volume is given by \(V=\frac{4}{3}\pi r^{3}\) What is the equation of the relative error \(\frac{\Delta V}{V}\) in measurement of the volume V ?
A. \(3\frac{\Delta r}{r}\)
B. \(4\frac{\Delta r}{r}\)
C. \(\frac{4}{3}\frac{\Delta r}{r}\)
D. \(\frac{1}{3}\frac{\Delta r}{r}\)
Answer : Option A
102. Kinetic energy K and linear momentum P are related as \(K=\frac{P^{2}}{2m}\). What is the equation of the relative error \(\frac{\Delta K}{K}\) in measurement of the K ? (mass in constant)
A. \(\frac{p}{\Delta p}\)
B. \(2\frac{\Delta p}{p}\)
C. \(\frac{p}{2\Delta p}\)
D. \(4\frac{\Delta p}{p}\)
Answer : Option B
103. Heat produced in a current carrying conducting wire is \(H=I^{2}Rt\) it percentage error in I, R and t is 2 % , 4 % and 2 % respectively then total percentage error in measurement of heat energy ________
A. 8%
B. 15%
C. 5%
D. 10%
Answer : Option D
Explanation :
heat energy \(H=I^{2}Rt\)
\(\Rightarrow \frac{\Delta H}{H}\times 100=\left [ 2\frac{\Delta I}{I}+\frac{\Delta R}{R}+\frac{\Delta t}{t} \right ]\times 100\)
\(=10\%\)
104. The resistance of two resistance wires are \(R_{1}=(100\pm 5)\Omega \) and \(R_{2}=(200\pm 7)\Omega \) are connected in series. find the maximum absolute error in the equivalent resistance of the combination.
105. The periodic time of simple pendulum is \(T=2\pi \sqrt{\frac{l}{g}}\) relative error in the measurement of \(T\) and \(l\) are \(\pm a\) and \(\pm b\) respectively find relative error in the measurement of \(g\)
A. a + b
B. 2b + a
C. 2a + b
D. a - b
Answer : Option C
Explanation :
\(g=4\pi ^{2}\frac{l}{T^{2}}\)
\(\frac{\Delta g}{g}=\frac{\Delta l}{l}+2\times \frac{\Delta l}{l}\)
\(=b+2a\)
106. The resistance \(R=\frac{V}{I}\) where \(V=100\pm 5\) volts and \(I=10\pm 0.3\) amperes calculate the percentage error in \(R\).
A. 8%
B. 10%
C. 12%
D. 14%
Answer : Option A
Explanation :
Resistance \(R=\frac{V}{I}\)
\(\frac{\Delta R}{R}=\frac{\Delta V}{V}+\frac{\Delta I}{I}\)
\(\frac{\Delta R}{R}=\frac{5}{100}+\frac{0.3}{10}\)
\(\frac{\Delta R}{R}\%=8\%\)
107. A physical quantity \(x\) is given by \(x=\frac{A^{4}B^{\frac{1}{4}}}{C^{3}D^{\frac{4}{3}}}\) due to which physical quantity produced the maximum percentage error in \(x\)
108. The number of significant figures in 0.000150 is
109. Which of the following numerical value have significant figure 4 ?
110. What is the number of significant figures in \(5.50\times 10^{3}\) ?