Answer
Verified
385.5k+ views
Hint: The time taken by the pendulum to move TO and FRO once is called its time period. The period of a simple pendulum depends upon various factors like the length of the suspension, gravitational acceleration, etc.
Complete step by step answer:
As we know that the time period of a simple pendulum is given by
$T = 2\pi \sqrt {\dfrac{l}{g}} $
Where T is the time period, l is the length of suspension of the pendulum and g is the acceleration due to gravity.
Now as we know the gravity of the moon is around $\dfrac{1}{6}$that of the earth so acceleration due to the gravity of the moon can also be assumed to be around $\dfrac{1}{6}$that of the earth.
As we know the acceleration due to gravity on earth is taken as $9.8m{\sec ^{ - 2}}$
So, the acceleration due to gravity on the moon can be taken as
${g_{moon}} = \dfrac{{{g_{earth}}}}{6}$
\[{g_{moon}} = \dfrac{{9.8}}{6} = 1.6m{\sec ^{ - 2}}\]
Now we need to find the length (l) we are given that time period of oscillation to be 2 seconds and we have calculated acceleration due to gravity $\left( {{g_{moon}}} \right)$
Substituting these values, we get,
$2 = 2\pi \sqrt {\dfrac{l}{{1.6}}} $
$ \to {\left( {\dfrac{2}{{2\pi }}} \right)^2} = \dfrac{l}{{1.6}}$
$ \to {\left( {\dfrac{1}{\pi }} \right)^2} = \dfrac{l}{{1.6}}$
$ \to l = \dfrac{{1.6}}{{{\pi ^2}}}$
$ \to l = 0.162m$
Hence, the length of the pendulum should be 0.162 meters to have a time period of 2 sec on the moon.
Note:
The gravity of the moon is $\dfrac{1}{6}$that of the earth. The acceleration due to gravity on the moon can be also assumed as $\dfrac{1}{6}$that of the earth. The time period of the pendulum greatly depends upon its length and acceleration due to gravity.
Complete step by step answer:
As we know that the time period of a simple pendulum is given by
$T = 2\pi \sqrt {\dfrac{l}{g}} $
Where T is the time period, l is the length of suspension of the pendulum and g is the acceleration due to gravity.
Now as we know the gravity of the moon is around $\dfrac{1}{6}$that of the earth so acceleration due to the gravity of the moon can also be assumed to be around $\dfrac{1}{6}$that of the earth.
As we know the acceleration due to gravity on earth is taken as $9.8m{\sec ^{ - 2}}$
So, the acceleration due to gravity on the moon can be taken as
${g_{moon}} = \dfrac{{{g_{earth}}}}{6}$
\[{g_{moon}} = \dfrac{{9.8}}{6} = 1.6m{\sec ^{ - 2}}\]
Now we need to find the length (l) we are given that time period of oscillation to be 2 seconds and we have calculated acceleration due to gravity $\left( {{g_{moon}}} \right)$
Substituting these values, we get,
$2 = 2\pi \sqrt {\dfrac{l}{{1.6}}} $
$ \to {\left( {\dfrac{2}{{2\pi }}} \right)^2} = \dfrac{l}{{1.6}}$
$ \to {\left( {\dfrac{1}{\pi }} \right)^2} = \dfrac{l}{{1.6}}$
$ \to l = \dfrac{{1.6}}{{{\pi ^2}}}$
$ \to l = 0.162m$
Hence, the length of the pendulum should be 0.162 meters to have a time period of 2 sec on the moon.
Note:
The gravity of the moon is $\dfrac{1}{6}$that of the earth. The acceleration due to gravity on the moon can be also assumed as $\dfrac{1}{6}$that of the earth. The time period of the pendulum greatly depends upon its length and acceleration due to gravity.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Why Are Noble Gases NonReactive class 11 chemistry CBSE
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
At which age domestication of animals started A Neolithic class 11 social science CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Write a letter to the principal requesting him to grant class 10 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE