Question

6. A pendulum completes 2 oscillations in 5 s.
(a) What is its time period ? (b) If g = 9.8 ms, find
its length.
Ans. (a) 2.5 s, (b) 1.55 m​

Answer 1

Explanation:

From unitary method if 2 oscillation complete in 5 sec then 1 oscillation complete in 5/2 = 2.5 s

$t =2\pi \sqrt{l \div g} \\ t = 2.5s \\ 2.5 = 2\pi \sqrt{l \div 9.8} \\square \: both \: the \: side \\ 2.5 \times 2.5 = 4 \times {3.14}^{2} \times l \div 9.8 \\ l = 2.5 \times 2.5 \times 9.8 \div 4 \times 3.14 \times 3.14 \\ l = 1.553m$