Question

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

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

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 $0.3\times 10=g_1-g_2$
$\therefore g_2=981-3=978cm/s^2$