Question

"On earth, you have a pendulum of length L that oscillates with period T. Your friend lives on a planet where the acceleration of gravity is four times as big as it is on the earth. What should be the length of a pendulum on your friend s planet so that it also oscillates with the same period T

Answer 1

Answer:

4L

Explanation:

Data provided in the question according to the question is as follows

Length = L

Gravity = G

For friend

Length = ?

Growth = 4G

Moreover,

$T_1 = T_2$

Based on the above information ,

Now we have to apply the simple pendulum formula which is shown below:

$T = 2\pi \frac{L}{G}$

Now equates these equations in both sides

$2\pi \frac{L}{G} = 2\pi \frac{L}{4G}$

So after solving this, the length of the pendulum is 4L

Answer 2

Answer:

the length of a pendulum on your friend s planet should be 4 times than that on earth

Explanation:

We know that time period of simple pendulum is given by

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

L= length of pendulum

g= acceleration due to gravity

therefore, Let T_1 and T_2 be the time period of the earth and other planet respectively.

$\frac{T_1}{T_2} =\sqrt(\frac{L_1}{L_2}\times\frac{g_2}{g_1})$

ATQ

T_1=T_2=T,   g_2=4g_1

Putting the values in above equation and solving we get

$\frac{L_1}{L_2} =\frac{1}{4}$