Maximum percentage errors in measurement of mass (M), radius (R) and angular velocity (omega) of a r

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1.Units, Dimensions and Measurement

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The maximum percentage errors in the measurement of mass (M), radius (R) and angular velocity $(\omega)$ of a ring are $2 \%, 1 \%$ and $1 \%$ respectively, then find the maximum percenta? error in the measurement of its moment of inertia $\left(I=\frac{1}{2} M R^{2}\right)$ about its geometric axis.

$4$

$5$

$6$

$7$

Solution

Moment of inertia ${\rm{(I) = M}}{{\rm{R}}^{\rm{2}}}{\rm{ }}$

$\therefore \,\,\frac{{\Delta I}}{I}\,\, \times \,\,100\,\, = \,\,\frac{{\Delta M}}{M}\,\, \times \,\,100\,\, + \;\;2\frac{{\Delta R}}{R}\,\, \times \,\,100$

$\, = \,\,2\% \,\, + \;\,\left( {2\,\, \times \,\,1\% } \right)\,\, = \,\,4\% $

the maximum percenta $\, = \,\,4\% $

Standard 11

Physics

The period of oscillation of a simple pendulum is given by $T = 2\pi \sqrt {\frac{l}{g}} $ where $l$ is about $100 \,cm$ and is known to have $1\,mm$ accuracy. The period is about $2\,s$. The time of $100$ oscillations is measured by a stop watch of least count $0.1\, s$. The percentage error in $g$ is ……… $\%$

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The mean time period of second's pendulum is $2.00s$ and mean absolute error in the time period is $0.05s$. To express maximum estimate of error, the time period should be written as

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Calculate the mean $\%$ error in five observation

$80.0,80.5,81.0,81.5,82$

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(AIIMS-2019)

The length and width of a rectangular room are measured to be $3.95 \pm 0.05 \,m$ and $3.05 \pm 0.05 \,m$, respectively. The area of the floor is ……………….. $m^2$

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(KVPY-2016)

In an experiment, the following observation's were recorded : $L = 2.820\, m, M = 3.00 \,kg, l = 0.087 \,cm$, Diameter $D = 0.041 \,cm$ Taking $g = 9.81$ $m/{s^2}$ using the formula , $Y=\frac{{4MgL}}{{\pi {D^2}l}}$, the maximum permissible error in $Y$ is ……… $\%$

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Solution

Similar Questions

The mean time period of second's pendulum is $2.00s$ and mean absolute error in the time period is $0.05s$. To express maximum estimate of error, the time period should be written as

Calculate the mean $\%$ error in five observation $80.0,80.5,81.0,81.5,82$

The length and width of a rectangular room are measured to be $3.95 \pm 0.05 \,m$ and $3.05 \pm 0.05 \,m$, respectively. The area of the floor is ……………….. $m^2$

In an experiment, the following observation's were recorded : $L = 2.820\, m, M = 3.00 \,kg, l = 0.087 \,cm$, Diameter $D = 0.041 \,cm$ Taking $g = 9.81$ $m/{s^2}$ using the formula , $Y=\frac{{4MgL}}{{\pi {D^2}l}}$, the maximum permissible error in $Y$ is ……… $\%$

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Calculate the mean $\%$ error in five observation

$80.0,80.5,81.0,81.5,82$