- Home
- Standard 11
- Physics
If there is an error of $1\%$ in calculation of mass of disc and $1.5\%$ error in radius, then $\%$ error in moment of inertia about an axis tangent to disc is .......... $\%$
$2.5 $
$4$
$3.5$
$5$
Solution
$I=\frac{5}{4} M R^{2}$
$\frac{\mathrm{dI}}{\mathrm{I}}=\frac{\mathrm{dM}}{\mathrm{M}}+2 \frac{\mathrm{d} \mathrm{R}}{\mathrm{R}}$
$=1 \%+2(1.5 \%)=1 \%+3 \%=4 \%$
Similar Questions
Three students $S_{1}, S_{2}$ and $S_{3}$ perform an experiment for determining the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.
| Student No. | Length of pendulum $(cm)$ | No. of oscillations $(n)$ | Total time for oscillations | Time period $(s)$ |
| $1.$ | $64.0$ | $8$ | $128.0$ | $16.0$ |
| $2.$ | $64.0$ | $4$ | $64.0$ | $16.0$ |
| $3.$ | $20.0$ | $4$ | $36.0$ | $9.0$ |
(Least count of length $=0.1 \,{m}$, least count for time $=0.1\, {s}$ )
If $E_{1}, E_{2}$ and $E_{3}$ are the percentage errors in $'g'$ for students $1,2$ and $3$ respectively, then the minimum percentage error is obtained by student no. ……. .
Students $I$, $II$ and $III$ perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum.
They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.
Least count for length $=0.1 \mathrm{~cm}$
Least count for time $=0.1 \mathrm{~s}$
| Student | Length of the pendulum $(cm)$ | Number of oscillations $(n)$ | Total time for $(n)$ oscillations $(s)$ | Time period $(s)$ |
| $I.$ | $64.0$ | $8$ | $128.0$ | $16.0$ |
| $II.$ | $64.0$ | $4$ | $64.0$ | $16.0$ |
| $III.$ | $20.0$ | $4$ | $36.0$ | $9.0$ |
If $\mathrm{E}_{\mathrm{I}}, \mathrm{E}_{\text {II }}$ and $\mathrm{E}_{\text {III }}$ are the percentage errors in g, i.e., $\left(\frac{\Delta \mathrm{g}}{\mathrm{g}} \times 100\right)$ for students $\mathrm{I}, \mathrm{II}$ and III, respectively,
