Question

Length of a second’s pendulum is 1 m whose time period is 2 s. Find the length of a pendulum whose time period is 1.4 s.

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Answer 1

Answer:

49 cm

Explanation:

at a certain place, the length of a seconds pendulum is 100cm. find the length of a pendulum whose time period is 1.4s.

t = time period

L = length of pendulum

other than length all other are constant

100 cm = 1m

A seconds pendulum is a pendulum whose period is precisely two seconds

$2 = 2\pi \sqrt{ \frac{1} { g} }$

let say x is length of pendulum with 1.4 sec time period

$1.4 = 2\pi \sqrt{ \frac{x} { g} } \\ 1.4 = 2\pi \sqrt{ \frac{1} { g} } \times \sqrt{x} \\ 1.4 = 2\sqrt{x}$

squaring both sides

1.96 = 4x

x = .49

.49 m = 49 cm

the length of a pendulum whose time period is 1.4s. is 49 cm