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The bob of a simple pendulum is imparted at a velocity \[5\,m{s^{ - 1}}\] when it is at its mean position. To what maximum vertical height will it rise on reaching to its extreme position if \[60\% \] of its energy is lost in overcoming friction of air?
A. \[5\,m\]
B. \[0.5\,m\]
C. \[0.25\,m\]
D. \[1\,m\]

Last updated date: 29th Feb 2024
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IVSAT 2024
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Hint: To solve this question we have to know about kinetic energy and potential energy. We know that, to speed up an item we need to apply power. To apply power, we need to tackle jobs. At the point when work is done on an article, energy is moved and the item moves with another consistent speed.

Complete step by step answer:
The energy that is moved is known as motor energy and it relies upon the mass and speed accomplished. As we probably are aware, an item can store energy because of its position.On account of a bow and a bolt, when the bow is drawn, it stores some measure of energy, which is answerable for the active energy it gains, when delivered.

We know that, when it is at mean position it will have a kinetic energy of \[0.5\,m{v^2}\].
So, kinetic energy is equal to \[0.5 \times m \times 5 \times 5 = 12.5\,mJ\]
\[60\% \] of this kinetic is lost hence remaining is equal to \[(40/100)12.5 \times m = 5m\].
Now, potential energy is equal to \[mgh = 5 \times m\].
\[h =\dfrac{5}{g} \\
\Rightarrow h= \dfrac{5}{10} \\
\therefore h= 0.5\,m \\ \]
Hence, the correct answer is option B.

Note: We can say, Potential energy is the energy held by an article due to its position comparative with different items, stresses inside itself, its electric charge, or different components. When it is uprooted from its harmony position, it acquires some measure of energy which we see as pressure we feel in our grasp after extending it. We can characterize expected energy as a type of energy that outcomes from the adjustment of its position or state.
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