Answer
Verified
429.9k+ views
Hint:A seconds pendulum is a simple pendulum whose time period is exactly equal to 2 seconds. The time period of a simple pendulum is given as $T=2\pi \sqrt{\dfrac{l}{g}}$, where l is the length of the pendulum and g is acceleration due to gravity.
Formula used:
$T=2\pi \sqrt{\dfrac{l}{g}}$
Here, T is the time period, l is the length of the pendulum and g is acceleration due to gravity.
Complete step by step answer:
A seconds pendulum is a simple pendulum whose time period is exactly equal to 2 seconds. It takes one second to swing in one direction and another one second to swing in the opposite direction. This way it completes one full oscillation in two seconds.The time period of a simple pendulum is given as $T=2\pi \sqrt{\dfrac{l}{g}}$, where l is the length of the pendulum and g is acceleration due to gravity.
On earth the acceleration due to gravity is g and the length of the pendulum is said to be l. Also, we know that the time period of a seconds pendulum is 2 seconds. Therefore,
$T=2\pi \sqrt{\dfrac{l}{g}}=2s$ …. (i).
The time period of the seconds pendulum on the other must be 2 seconds also. It is given that the acceleration due to the gravity of this planet is $\dfrac{g}{4}$. Let its length be l’.
Then we write its time period as $T=2s=2\pi \sqrt{\dfrac{l'}{\dfrac{g}{4}}}$
$2\pi \sqrt{\dfrac{4l'}{g}}=2$ …. (ii).
Now, divide (ii) by (i).
$\dfrac{2\pi \sqrt{\dfrac{4l'}{g}}}{2\pi \sqrt{\dfrac{l}{g}}=2}=\dfrac{2}{2}$
$\Rightarrow \sqrt{\dfrac{4l'}{l}}=1$
$\Rightarrow \dfrac{4l'}{l}=1$
$\therefore l'=\dfrac{l}{4}$.
This means that the required length of the seconds pendulum on the other planet is equal to $\dfrac{l}{4}$.
Hence, the correct option is C.
Note:From the formula for the time period of a simple pendulum, we understand that the time period of a pendulum only depends on its length and the acceleration due to gravity at its location. It is interesting to know that the time period of a pendulum is independent of its mass.
Formula used:
$T=2\pi \sqrt{\dfrac{l}{g}}$
Here, T is the time period, l is the length of the pendulum and g is acceleration due to gravity.
Complete step by step answer:
A seconds pendulum is a simple pendulum whose time period is exactly equal to 2 seconds. It takes one second to swing in one direction and another one second to swing in the opposite direction. This way it completes one full oscillation in two seconds.The time period of a simple pendulum is given as $T=2\pi \sqrt{\dfrac{l}{g}}$, where l is the length of the pendulum and g is acceleration due to gravity.
On earth the acceleration due to gravity is g and the length of the pendulum is said to be l. Also, we know that the time period of a seconds pendulum is 2 seconds. Therefore,
$T=2\pi \sqrt{\dfrac{l}{g}}=2s$ …. (i).
The time period of the seconds pendulum on the other must be 2 seconds also. It is given that the acceleration due to the gravity of this planet is $\dfrac{g}{4}$. Let its length be l’.
Then we write its time period as $T=2s=2\pi \sqrt{\dfrac{l'}{\dfrac{g}{4}}}$
$2\pi \sqrt{\dfrac{4l'}{g}}=2$ …. (ii).
Now, divide (ii) by (i).
$\dfrac{2\pi \sqrt{\dfrac{4l'}{g}}}{2\pi \sqrt{\dfrac{l}{g}}=2}=\dfrac{2}{2}$
$\Rightarrow \sqrt{\dfrac{4l'}{l}}=1$
$\Rightarrow \dfrac{4l'}{l}=1$
$\therefore l'=\dfrac{l}{4}$.
This means that the required length of the seconds pendulum on the other planet is equal to $\dfrac{l}{4}$.
Hence, the correct option is C.
Note:From the formula for the time period of a simple pendulum, we understand that the time period of a pendulum only depends on its length and the acceleration due to gravity at its location. It is interesting to know that the time period of a pendulum is independent of its mass.
Recently Updated Pages
Write the IUPAC name of the given compound class 11 chemistry CBSE
Write the IUPAC name of the given compound class 11 chemistry CBSE
Write the IUPAC name of the given compound class 11 chemistry CBSE
Write the IUPAC name of the given compound class 11 chemistry CBSE
Write the IUPAC name of the given compound class 11 chemistry CBSE
Write the IUPAC name of the given compound class 11 chemistry CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Distinguish between the following Ferrous and nonferrous class 9 social science CBSE
The term ISWM refers to A Integrated Solid Waste Machine class 10 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Which is the longest day and shortest night in the class 11 sst CBSE
In a democracy the final decisionmaking power rests class 11 social science CBSE