Question

Due to a technical malfunction a space explorer had to crash land on Planet-X. She manages to fix her space ship and now she is preparing for launch. However she needs to know the gravitational acceleration on the surface of the planet in order to take off successfully. She builds a mathematical pendulum out of a piece of string and a left over steel bolt. The bolt has a mass of 35.5 g, and the string is 133 cm long. She attaches the pendulum to a fixed point and she lets it swing. She counts 12 complete oscillations in a time period of 70.7 seconds. What is the gravitational acceleration on the surface of Planet-X

Answer 1

the gravitational acceleration of the Xplanet is 1.344m/s^2

Step-by-step explanation:

You can use the formula for the calculation of the frequency of a pendulum, in order to find an expression for the gravitational constant:

`f=(1)/(2\pi)\sqrt{(g)/(l)}\\\\g=4\pi^2 f^2l`

Where you can notice that mass ob the object does not influence of the gravitatiolan acceleration. By the information of the question, you have the values of f and l. By replacing these values (with units of meter and seconds) you obtain:

`f=(12)/(70.7)=0.16s^(-1)\\\\g=4\pi^2(0.16s^(-1))^2(1.33m)=1.344(m)/(s^2)`

Hence, the gravitational acceleration of the Xplante is 1.344m/s^2

Answer 2

The gravitational acceleration on the surface of Planet-X is 1.5
`ms^(-2)`

Step-by-step explanation:

Firstly, we are to list out the parameters given:

Mass (m) = 35.5 g, Length of string (L) = 133 cm = 1.33 m, t = 70.7 seconds for 12 oscillations, T = 70.7 ÷ 12 = 5.89 seconds

The formula for calculating the period of a simple pendulum (assuming the angle of deflection is lesser than 15º) is given by:

`T=2\pi\sqrt{(L)/(g)}\\`

We want to calculate for the gravitational acceleration (g), hence, we have to make g the subject of the formula

`g=4\pi^(2)(L)/(T^(2))\\`

Substitute the parameters into the equation, we have:

g =
`4\pi^(2)` * 1.33 ÷
`5.89^(2)` = 1.51

g = 1.5
`ms^(-2)`

The gravitational acceleration on the surface of Planet-X is 1.5
`ms^(-2)`