Question

The length of the seconds pendulum is decreased by $0.3\, cm$ when it is shifted to Chennai from London. If the acceleration due to gravity at London is $ 981\,cm/{{s}^{2}}, $ the acceleration due to gravity at Chennai is (assume $ {{n}^{2}}=10 $ )

• A. $ 981\,cm/{{s}^{2}} $
• B. $ 978\,cm/{{s}^{2}} $
• C. $ 984\,cm/{{s}^{2}} $
• D. $ 975\,cm/{{s}^{2}} $

Answer 1

Answer: (B)

$L_{1}=\frac{g_{1} T^{2}}{4 \pi^{2}} =\frac{g_{1}}{\pi^{2}}$
$L_{2} =\frac{g_{2} T^{2}}{4 \pi^{2}}=\frac{g_{2}}{\pi^{2}}$
Since, length is decreased, $g_{2}$ is less than $g_{1}$.
$\therefore L_{1}-L_{2} =\frac{g_{1}-g_{2}}{\pi^{2}} $
or $ \left(L_{1}-L_{2}\right) \pi^{2} =g_{1}-g_{2} $
or $ 0.3 \times 10 =g_{1}-g_{2} $
$\therefore g_{2} =981-3=978 \,cm / s ^{2}$