Question

The change in the length of a simple pendulum of length $1m$, when its period of oscillation changes from $2s$ to $1.5s$ is:

• A. increased by $\frac{7}{8}m$
• B. decreased by $4\frac{7}{8}m$
• C. increased by$\frac{7}{16}m$
• D. decreased by $\frac{7}{16}m$

Answer 1

Answer: (D)

decreased by $\frac{7}{16}m$

Given, $T_1=2sec$

$L_1=1m$

$T_2=1.5sec$

$T=2\pi \sqrt{\frac{L}{g}}$

$T\alpha \sqrt{L}$

$\frac{T_1}{\sqrt{L_2}}=\frac{T_2}{\sqrt{L_2}}$

$\therefore \frac{2}{\sqrt{1}}=\frac{1.5}{\sqrt{L_2}}$

$L_2=\frac{9}{16}$

$L_1-L_2=1-\frac{9}{16}$

$=\frac{7}{16}$

$\therefore$ length decreased by $\frac{7}{16}m.$