Question

Suppose you are an astronaut and need to find the acceleration due to gravity on an asteroid using a pendulum. The period of the pendulum is 20 seconds and the length of the pendulum is 10 cm. What is g?

Answer 1

The value of the acceleration due to gravity (g) on the asteroid is equal to 9.86 × 10⁻³ ms⁻².

Given:

The time period of the pendulum = 20 seconds

The length of the pendulum = 10 cm

To Find:

The value of the acceleration due to gravity (g).

Solution:

→ The relationship between the acceleration due to gravity (g), the length of the pendulum (L) and the time period of the pendulum (T) are given as:

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

→ In the given question:

The time period of the pendulum (T) = 20 seconds

The length of the pendulum (L) = 10 cm = 0.1 m

Let the value of the acceleration due to gravity on the asteroid be 'g'.

                           $\boldsymbol{\because T=2\pi \sqrt{\frac{L}{g} } }\\\\\boldsymbol{\therefore T^{2} =4\pi^{2}\frac{L}{g} }\\\\\boldsymbol{\therefore g =4\pi^{2}\frac{L}{T^{2} } }\\\\\boldsymbol{\therefore g =4\pi^{2}\frac{(0.1)}{(20)^{2} } }\\\\\boldsymbol{\therefore g =4\times3.14\times3.14\times\frac{(0.1)}{(20)^{2} } }\\\\\boldsymbol{\therefore g =39.44\times\frac{(0.1)}{(400)} }\\\\\boldsymbol{\therefore g =\frac{3.944}{400} }\\\\\boldsymbol{\therefore g =9.86\times10^{-3} \:ms^{-2} }$

→ The value of 'g' comes out to be equal to 9.86 × 10⁻³ ms⁻².

Therefore the value of the acceleration due to gravity (g) on the asteroid comes out to be equal to 9.86 × 10⁻³ ms⁻².

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