Question:
The physical quantity \(P=\frac{a^{3}b^{2}}{c^{1/3}d^{1/4}}\), where the percentage error in a, b, c, and d are \(1\%\), \(\frac{3}{2}\%\), \(3\%\), and \(2\%\) respectively. Then the percentage error in P is
The physical quantity \(P=\frac{a^{3}b^{2}}{c^{1/3}d^{1/4}}\), where the percentage error in a, b, c, and d are \(1\%\), \(\frac{3}{2}\%\), \(3\%\), and \(2\%\) respectively. Then the percentage error in P is
Show Hint
For a product of powers, the maximum percentage error is the sum of each percentage error multiplied by its power.
Updated On: Nov 12, 2026
- \(14\ \%\)
- \(14.5\ \%\)
- \(7\ \%\)
- \(7.5\ \%\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
For \(P=\dfrac{a^{3}b^{2}}{c^{1/3}d^{1/4}}\), the maximum percentage error adds each percentage error multiplied by the magnitude of its power.
Step 2: Calculation
\(\dfrac{\Delta P}{P}\times100=3(1)+2\left(\dfrac{3}{2}\right)+\dfrac{1}{3}(3)+\dfrac{1}{4}(2)\)
\(=3+3+1+0.5\)
Step 3: Result
The percentage error in P is \(7.5\%\).
Final Answer:
The percentage error in P is 7.5 percent. \[ \boxed{\text{(D) }7.5\ \%} \]
For \(P=\dfrac{a^{3}b^{2}}{c^{1/3}d^{1/4}}\), the maximum percentage error adds each percentage error multiplied by the magnitude of its power.
Step 2: Calculation
\(\dfrac{\Delta P}{P}\times100=3(1)+2\left(\dfrac{3}{2}\right)+\dfrac{1}{3}(3)+\dfrac{1}{4}(2)\)
\(=3+3+1+0.5\)
Step 3: Result
The percentage error in P is \(7.5\%\).
Final Answer:
The percentage error in P is 7.5 percent. \[ \boxed{\text{(D) }7.5\ \%} \]
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