Question

A simple pendulum of length \(l_1\) has periodic time \(2.4\) s. Another simple pendulum of length \(l_2 < l_1\), has periodic time \(1.8\) s. The periodic time of simple pendulum of length \((l_1-l_2)\) is nearly

• A. \(1.2\) s
• B. \(1.4\) s
• C. \(1.6\) s
• D. \(1.8\) s

Hint:

T squared is proportional to length, so lengths subtract in T squared.

Answer 1

The Correct Option is C

Step 1: Find the lengths:
Take $g = 9.8$ m/s$^2$: $l_1 = \frac{9.8\times5.76}{4\pi^2} = 1.43$ m and $l_2 = \frac{9.8\times3.24}{4\pi^2} = 0.80$ m.

Step 2: Difference:
$l_1 - l_2 = 0.63$ m.

Step 3: New period:
$T = 2\pi\sqrt{\frac{0.63}{9.8}} = 2\pi\times0.2535 = 1.59$ s, about 1.6 s.

Final Answer:
The period is about 1.6 s, option (C). \[ \boxed{1.6\text{ s}} \]