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

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

Step-by-step explanation:

We know that time period of simple pendulum is given by

`T= 2\pi\sqrt{(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.

`(T_1)/(T_2) =\sqrt((L_1)/(L_2)*(g_2)/(g_1))`

ATQ

T_1=T_2=T, g_2=4g_1

Putting the values in above equation and solving we get

`(L_1)/(L_2) =(1)/(4)`

Answer 2

4L

Step-by-step 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 (L)/(G)`

Now equates these equations in both sides

`2\pi (L)/(G) = 2\pi (L)/(4G)`

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