The bob of a pendulum of length 2 m lies at P. When it reaches Q, it loses 10 % of its total energy due to air resistance. The velocity at Q is
A pendulum is a weight suspended from a fixed point, allowing it to swing freely under gravity’s influence. It demonstrates periodic motion, with applications in clocks, seismology and experiments to study harmonic motion and Earth’s gravitational acceleration.
Class 11 Physics, Chapter 5 focuses on the concepts of work, energy and power, essential for understanding mechanics. It covers definitions, formulas and the relationship between these quantities, alongside practical applications and problem-solving techniques. The chapter prepares students for CBSE EXAM 2024-25 by emphasizing key principles and calculations critical to the study of physical sciences and engineering.
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We first need to understand the system. When the pendulum is at point P, it has maximum potential energy and no kinetic energy because it is momentarily at rest. Now, as the pendulum swings down to point Q, the potential energy gets converted into kinetic energy. To find the velocity of the pendulum bob at point Q after losing 10% of its energy due to air resistance, we begin with understanding the system.
However, during this process, the pendulum loses 10% of its total mechanical energy to air resistance. Thus, only 90% of the initial total energy is available for conversion into kinetic energy at point Q. The energy conversion results in the pendulum bob gaining speed as it moves downward.
We can calculate the velocity at point Q. The lost energy is the one that reduces the kinetic energy the bob can have at the lowest point. The remaining energy translates into kinetic energy, which can be expressed in terms of the mass of the bob and its velocity.
Ultimately, taking into consideration the energy transformations and the energy loss effect we observe that the pendulum bob at point Q will have a velocity of 6 meters per second. The answer is, therefore, 6 m/s.
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