A physical quantity P is related to four observable a, b, c and d as follows \(P=\frac{a^{3}b^{2}}{\sqrt{c}d}\). The percentage error in the measurement of a, b, c and d are \(1\%\), \(3\%\), \(4\%\) and \(2\%\) respectively. What is the percentage error in the quantity P, if the value of P is being calculated using the above equation turns out to be \(3.763\), to what value should you round off the result?
Ans: \(\frac{\Delta P}{P}\times100\%=\pm13\%\).
The heat dissipated in a resistance can be obtained by the measurement of resistance, the current and time. If the maximum error in the measurement of those quantities are \(1\%\), \(2\%\) and \(1\%\) respectively. Then, what will be the maximum error in the measurement of the dissipated heat \(Q=\frac{I^{2}Rt}{4.2} cal\).
Ans: \(\frac{\Delta Q}{Q}\times100\%=6\%\).
For the calculation of Young’s Modulus \(Y=\frac{4Mg}{\pi d^{2}\frac{L}{l}}\) for a wire. Following observations were recorded \(L=2.890\), \(M=3.00\), \(d=0.082\) and \(g=9.81\), \(l=0.087\). Calculate: the maximum percentage error in the value of Y and mention which physical quantity causes maximum error?
Ans: \(\frac{\Delta Y}{Y}\times\%=\pm3.956\%\).
The radius of a sphere is measured to be \(\left(5.3\pm0.1\right)cm\). Calculate: the percentage error in measurement of its volume.
Ans: \(6\%\).
Two resistors of resistances \(R_{1}=\left(4\pm 0.5\right)\Omega\) and \(R_{2}=\left(16\pm 0.5\right)\Omega\) are connected in (i) Series and (ii) Parallel. Find: the equivalent resistance in each case with limits ot percentage error.
A potential difference, \(V=\left(2.0\pm 1\right)volt\) is applied across a resistor \(R=\left(8.0\pm2\right)\Omega\). Find: the current with in error limits.
The measurement of the diameter of a cylinder is \(\left(1.60\pm 0.01\right)cm\) and the length is \(\left(5.0\pm 0.1\right) cm\). Calculate: percentage error in its volume?
Ans: \(\frac{\Delta V}{V}\times100\%=\pm3.25\%\).
A body travels uniformly with a distance of \(\left(13.8\pm 0.2\right) metre\) in a time \(\left(4.0\pm 0.3\right) seconds\). Calculate: its velocity with error limits. What is the percentage error in velocity?
Ans: \(V=\left(3.4\pm0.3\right)\frac{m}{s}\).
What will be the focal length of a mirror if the object distance is \(\left(50.1\pm 0.5\right)cm\) and image distance is \(\left(20.1\pm 0.2\right)cm\)? Calculate: the focal length with error limits?
Ans: \(f=\left(14.3\pm0.4\right)cm\).
The radius of a sphere is given as \(\left(2.1\pm 0.5\right)cm\). Calculate: its surface area with error limits.
