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2 years ago

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If you know that the period of a pendulum is 1.87 seconds, what is the length of that pendulum? (Assume that we are on Earth and

that gravity is 9.81 meters/second².) Select one of the options below as your answer: A. 0.87 centimeters B. 2.1 meters C. 1.6 meters D. 0.87 meters E. 8.3 meters

2 answers:

shepuryov [24]2 years ago

8 0

Period of an ideal simple pendulum = 2π √(L / G)

1.87 = 2π √ (L / 9.81)

Divide each side by 2π : (1.87 / 2π) = √ (L / 9.81)

Square each side: (1.87 / 2π)² = L / 9.81

Multiply each side by 9.81 : L = (9.81) (1.87 / 2π)² = <em> 0.869 meter</em>

Choice 'D' is the closest one.

mote1985 [20]2 years ago

8 0

Answer : The correct option is, (D) 0.87 meters

Solution :

Formula used :

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

where,

T = time period of a pendulum = 1.87 seconds

L = length of the pendulum = ?

g = gravity on earth = $9.8m/s^2$

Now put all the given values in the above formula, we get the length of the pendulum.

$1.87s=2\times \frac{22}{7}\times \sqrt{\frac{L}{9.8m/s^2}}$

$0.2975=\sqrt{\frac{L}{9.8m/s^2}}$

Now squaring on both the sides, we get

$L=0.868m=0.87m$

Therefore, the length of the pendulum is, 0.87 meters.

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