Question

The length of the second's pendulum is decreased by $0.3$cm 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?

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

Answer 1

The correct option is B $978cm/s^2$

Time period of second's pendulum $T=2s$
$L_1=\frac{g_1{T}^2}{4{\pi }^2}=\frac{g_1}{{\pi }^2}$ $(\because T=2s)$
Similarly, $L_2=\frac{g_2{T}^2}{4{\pi }^2}=\frac{g_2}{{\pi }^2}$
Since, length is decreased, $g_2$ is less than $g_1$.
$\therefore L_1-L_2=\frac{g_1-g_2}{{\pi }^2}$
or $(L_1-L_2){\pi }^2=g_1-g_2$
or $0.3\times 10=g_1-g_2$
$\therefore g_2=981-3=978cm/s^2$.