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)

$978\,cm/{{s}^{2}}$

Answer 2

$L_{1}=\frac{g_{1} T^{2}}{4 \pi^{2}} =\frac{g_{1}}{\pi^{2}}$ $L_{2} =\frac{g_{2} T^{2}}{4 \pi^{2}}=\frac{g_{2}}{\pi^{2}}$ 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 $0.3 \times 10 =g_{1}-g_{2}$ $\therefore g_{2} =981-3=978 \,cm / s ^{2}$