Physics - SHM Question with Solution | TestHub

$\text{T}=2\pi \sqrt{\frac{l}{\text{g}}}$or$\text{T}\propto \frac{1}{\sqrt{\text{g}}}$

$\therefore \frac{{\text{T}}^{\prime }}{\text{T}}=\sqrt{\frac{\text{g}}{{\text{g}}^{\prime }}}$

But${\text{g}}^{\prime }=\frac{\text{g}}{{\left(1+\frac{\text{h}}{\text{R}}\right)}^2}$or$\frac{{\text{g}}^{\prime }}{\text{g}}=\frac{1}{{\left(1+\frac{\text{h}}{\text{R}}\right)}^2}$

$\therefore \frac{{\text{T}}^{\prime }}{\text{T}}=\left(1+\frac{\text{h}}{\text{R}}\right)$

or${\text{T}}^{\prime }=\text{T}\left(1+\frac{\text{h}}{\text{R}}\right)$

Since,${\text{T}}^{\prime }>\text{T}$, the clock will lose the time.

$\therefore \Delta \text{T}={\text{T}}^{\prime }-\text{T}=\text{T}\left(\frac{\text{h}}{\text{R}}\right)$

$\therefore$Time lost in$t=1$day is

$=\frac{\left(24\times 3600\right)\left(200\right)}{\text{6.4}\times 10^6}\text{ s}=\text{2.7 s}$