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Current Question (ID: 11270)
Question:
$\text{A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector } \vec{a} \text{ is correctly shown in:}$
Options:
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1. $\text{Option 1: Acceleration vector pointing up and to the left}$
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2. $\text{Option 2: Acceleration vector pointing down and to the right}$
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3. $\text{Option 3: Acceleration vector pointing down and to the left}$
(Correct)
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4. $\text{Option 4: Acceleration vector pointing straight down}$
Solution:
$\text{The correct answer is Option 3.}$ $\text{For a simple pendulum oscillating without damping, the acceleration has two components:}$ $a_c = \text{Centripetal acceleration (directed toward the center of circular motion)}$ $a_t = \text{Tangential acceleration (directed tangentially to the path)}$ $a_N = \text{Net acceleration = Resultant of } a_c \text{ and } a_t$ $\text{When the displacement is less than maximum (i.e., the bob is not at the extreme position), the pendulum bob has both:}$ $\text{1. Centripetal acceleration directed toward the pivot point (upward along the string)}$ $\text{2. Tangential acceleration due to the restoring force component (directed toward equilibrium position)}$ $\text{The net acceleration is the vector sum of these two components. At a position where the bob is displaced to the right of equilibrium and moving, the net acceleration vector points down and to the left, directing the bob back toward the equilibrium position while accounting for the circular motion.}$ $\text{This combination results in the acceleration vector shown in Option 3, which correctly represents the direction of the net acceleration when the bob is at an intermediate position during its oscillation.}$
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