Question

7. The time periods of two simple pendulums at a place are in the ratio 2 : 1. What will be the ratio of their lengths ? Ans. 4:1

8. It takes 0-2 s for a pendulum bob to move from mean position to one end. What is the time period of pendulum? Ans. 0-8 S

9. How much time does the bob of a seconds' pendulum take to move from one extreme of its oscillation to the other extreme ?
Ans. ls​

Answer 1

$\bold{7) \: T_1:T_2::2:1}$

$\bold{2\pi \sqrt{ \frac{l_1}{g} } :2\pi\sqrt{ \frac{l_2}{g} }::2:1}$

$\bold{\sqrt{l_1} : \sqrt{l_2}::2:1}$

square both sides

$\bold{( \frac{ \sqrt{l_1} }{\sqrt{l_2}} ) {}^{2} = ( \frac{2}{1} ) {}^{2}}$

$\bold{l_1:l_2::4:1}$

8) time period will be time between the bob going from one mean position to another and then return back to mean position

therefore T = 0.8 s

9) We know that the time period of seconds' pendulum is 2 seconds

∴ The time taken for a seconds' pendulum to make half oscillation is

$\bold{ \frac{1}{2} \times 2 \: seconds = 1 \: second}$