Question

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

Answer 1

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  =  0.869 meter

                                              Choice 'D' is the closest one.

Answer 2

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.