$Assertion$ : When percentage errors in the measurement of mass and velocity are $1\%$ and $2\%$ respectively,the percentage error in $K.E.$ is $5\%$.
$Reason$ : $\frac{{\Delta E}}{E} = \frac{{\Delta m}}{m} + \frac{{2\Delta v}}{v}$
$Reason$ : $\frac{{\Delta E}}{E} = \frac{{\Delta m}}{m} + \frac{{2\Delta v}}{v}$
- AIf both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
- BIf both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
- CIf the Assertion is correct but Reason is incorrect.
- DIf both the Assertion and Reason are incorrect.
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Similar Questions
$A$ student determined Young's Modulus of elasticity using the formula $Y = \frac{M g L^{3}}{4 b d^{3} \delta}$. The value of $g$ is taken to be $9.8 \, m/s^2$, without any significant error. His observations are as follows:
Physical Quantity Least count and Observed value Mass $(M)$ $1 \, g$ and $2 \, kg$ Length of bar $(L)$ $1 \, mm$ and $1 \, m$ Breadth of bar $(b)$ $0.1 \, mm$ and $4 \, cm$ Thickness of bar $(d)$ $0.01 \, mm$ and $0.4 \, cm$ Depression $(\delta)$ $0.01 \, mm$ and $5 \, mm$
Then the fractional error in the measurement of $Y$ is:
| Physical Quantity | Least count and Observed value |
| Mass $(M)$ | $1 \, g$ and $2 \, kg$ |
| Length of bar $(L)$ | $1 \, mm$ and $1 \, m$ |
| Breadth of bar $(b)$ | $0.1 \, mm$ and $4 \, cm$ |
| Thickness of bar $(d)$ | $0.01 \, mm$ and $0.4 \, cm$ |
| Depression $(\delta)$ | $0.01 \, mm$ and $5 \, mm$ |
Then the fractional error in the measurement of $Y$ is:
DifficultJEE MAIN 2021
View SolutionThe period of oscillation of a simple pendulum is $T = 2\pi \sqrt{\frac{l}{g}}$. The measured value of $l$ is $20.0 \text{ cm}$ known to $1 \text{ mm}$ accuracy,and the time for $100$ oscillations of the pendulum is found to be $90 \text{ s}$ using a wristwatch of $1 \text{ s}$ resolution. The accuracy in the determination of $g$ is ........ $\%$
DifficultJEE MAIN 2015
View SolutionThe density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5\%$ and $1\%$,the maximum error in determining the density is ........ $\%$
If the absolute error is $0.05 \ m$ for a measured length of $5 \ m$, what is the percentage error (in $\%$)?
The pressure on a square plate is measured by measuring the force acting on the plate and the length of the sides of the plate. If the maximum percentage error in the measurement of force and length are $4 \%$ and $2 \%$ respectively,what is the percentage error in the measurement of pressure (in $\%$)?
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