- Home
- Standard 11
- Physics
13.Oscillations
hard
The acceleration due to gravity is found upto an accuracy of $4 \,\%$ on a planet. The energy supplied to a simple pendulum to known mass ' ${m}$ ' to undertake oscillations of time period $T$ is being estimated. If time period is measured to an accuracy of $3\, \%$, the accuracy to which ${E}$ is known as $..........\,\%$
A$85$
B$31$
C$24$
D$14$
(JEE MAIN-2021)
Solution
${T}=2 \pi \sqrt{\frac{\ell}{{g}}} \Rightarrow \ell=\frac{{T}^{2} {g}}{4 \pi^{2}}$
${E}={mg} \ell \frac{\theta^{2}}{2}={mg}^{2} \frac{{T}^{2} \theta^{2}}{8 \pi^{2}}$
$\frac{{dE}}{{E}}=2\left(\frac{{dg}}{{g}}+\frac{{dT}}{{T}}\right)$
$=(4+3)=14\, \%$
${E}={mg} \ell \frac{\theta^{2}}{2}={mg}^{2} \frac{{T}^{2} \theta^{2}}{8 \pi^{2}}$
$\frac{{dE}}{{E}}=2\left(\frac{{dg}}{{g}}+\frac{{dT}}{{T}}\right)$
$=(4+3)=14\, \%$
Standard 11
Physics
