Question:
In a certain system, the quantities A and B are measured as \(8\pm 0.08\) and \(6\pm 0.06\) respectively. Let \(x=AB\), \(y=A+B\) and \(z=A-B\). The correct order of % error in \(x\), \(y\) and \(z\) is
In a certain system, the quantities A and B are measured as \(8\pm 0.08\) and \(6\pm 0.06\) respectively. Let \(x=AB\), \(y=A+B\) and \(z=A-B\). The correct order of % error in \(x\), \(y\) and \(z\) is
Show Hint
Percentage errors add for a product, while absolute errors add for a sum or a difference.
Updated On: Nov 12, 2026
- \(x=y>z\)
- \(x\lt z\lt y\)
- \(z>x>y\)
- \(x>z>y\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
For a product, fractional errors add. For a sum or a difference, absolute errors add and then the percentage is taken on the result.
Step 2: Error in x = AB
\(\dfrac{\Delta A}{A}=\dfrac{0.08}{8}=1\%\) and \(\dfrac{\Delta B}{B}=\dfrac{0.06}{6}=1\%\)
So the error in \(x\) is \(1\%+1\%=2\%\).
Step 3: Error in y = A + B
\(y=14\) and \(\Delta y=0.08+0.06=0.14\)
% error in \(y=\dfrac{0.14}{14}\times100=1\%\)
Step 4: Error in z = A - B
\(z=2\) and \(\Delta z=0.14\)
% error in \(z=\dfrac{0.14}{2}\times100=7\%\)
Step 5: Compare the options
The errors are \(7\%>2\%>1\%\), that is \(z>x>y\).
Final Answer:
The percentage errors are in the order z > x > y. \[ \boxed{\text{(C) }z>x>y} \]
For a product, fractional errors add. For a sum or a difference, absolute errors add and then the percentage is taken on the result.
Step 2: Error in x = AB
\(\dfrac{\Delta A}{A}=\dfrac{0.08}{8}=1\%\) and \(\dfrac{\Delta B}{B}=\dfrac{0.06}{6}=1\%\)
So the error in \(x\) is \(1\%+1\%=2\%\).
Step 3: Error in y = A + B
\(y=14\) and \(\Delta y=0.08+0.06=0.14\)
% error in \(y=\dfrac{0.14}{14}\times100=1\%\)
Step 4: Error in z = A - B
\(z=2\) and \(\Delta z=0.14\)
% error in \(z=\dfrac{0.14}{2}\times100=7\%\)
Step 5: Compare the options
The errors are \(7\%>2\%>1\%\), that is \(z>x>y\).
Final Answer:
The percentage errors are in the order z > x > y. \[ \boxed{\text{(C) }z>x>y} \]
Was this answer helpful?
0
0
Top MHT CET Physics Questions
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is
- If $M_z$ = magnetization of a paramagnetic sample, $B$ = external magnetic field, $T$ = absolute temperature, $C$ = curie constant then according to Curie�s law in magnetism, the correct relation is
- In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $'t'$ second. The frequency of vibration of air column is
- In a parallel plate capacitor, the capacity increases if
View More Questions
Top MHT CET Error Analysis Questions
- In the process of space communication, use of modem is necessary. In which one of the following modes modem acts as a modulator and a demodulator respectively?
- The period of oscillating simple pendulum is $T = 2\pi \sqrt{\frac{l}{g}}$ where length ' $l$ ' is $100\text{ cm}$ with error $1\text{ mm}$ . Period is $2\text{ second}$. The time of $100$ oscillations is measured by a stopwatch of least count $0.1\text{s}$. The percentage error in gravitational acceleration ' $g$ ' is
- A student measures time for 20 oscillations of a simple pendulum as \(30\text{ s}, 32\text{ s}, 35\text{ s}\) and \(35\text{ s}\) . If the minimum division in the measuring clock is \(1\text{ s}\) , then correct mean time (in second) is
- The initial and final temperatures of water as recorded by an observer are $(38.6 \pm 0.2)^\circ\text{C}$ and $(82.3 \pm 0.3)^\circ\text{C}$. The rise in temperature with proper error limits is
- The initial and final temperatures of water as recorded by an observer are $(38.6 \pm 0.2)^\circ\text{C}$ and $(82.3 \pm 0.3)^\circ\text{C}$. The rise in temperature with proper error limits is
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions