$\begin{gathered}
{a_c} = \frac{{{v^2}}}{R} = {n^2}R{t^2} \hfill \\
{v^2} = {n^2}{R^2}{t^2} \hfill \\
\end{gathered} $
$v = nRt$
${a_c} = \,\frac{{dv}}{{dt}} = nR$
Power $= M{a_c}v = MnRnRt = M{n^2}{R^2}t.$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
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,
