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Work, Energy, and Power — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWork, Energy, and Power5 Marks
Question
The bob of a pendulum is released from a horizontal position. If the length of the pendulum is $1.5m$, what is the speed with which the bob arrives at the lowermost point, given that it dissipated $5\%$ of its initial energy against air resistance?
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Answer

Length of the pendulum, l = 1.5m Mass of the bob = m Energy dissipated = 5% According to the law of conservation of energy, the total energy of The system remains constant. At the horizontal position: Potential energy of the bob, $E_P$ = mgl Kinetic energy of the bob, $E_K = 0$ Total energy = mgl …(i) At the lowermost point (mean position): Potential energy of the bob, $E_P = 0$ Kinetic energy of the bob, $\text{EK}= \frac{1}{2}\text{mv}^2$ Total energy $\text{E}_{\text{x}}=\Big(\frac{1}{2}\Big)\text{mv}^2\ ...(\text{ii})$ As the bob moves from the horizontal position to the lowermost point, 5% of its energy gets dissipated. The total energy at the lowermost point is equal to 95% of the total energy at the horizontal point, i.e. $\frac{1}{2}\text{mv}^2 =\frac{95}{100}\text{mgl}$
$\therefore\text{ v}=\Big(2 \times 95 \times 1.5 \times \frac{9.8 }{100}\Big)^{\frac{1}{2}}$
$= 5.28 \text{m/s}$

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