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Current Question (ID: 11269)
Question:
$\text{A simple pendulum of mass } m \text{ swings about point } B \text{ between extreme positions } A \text{ and } C\text{. Net force acting on the bob at these three points is correctly shown by:}$
Options:
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1. $\text{Option 1: Forces at A and C point toward B, force at B points downward}$
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2. $\text{Option 2: Forces at A and C point toward B, force at B points upward}$
(Correct)
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3. $\text{Option 3: Forces at A and C point toward B, force at B points upward}$
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4. $\text{Option 4: Forces at A and C point toward B, force at B points downward}$
Solution:
$\text{Hint: Net force on a body in SHM is towards the mean position.}$ $\text{Step 1: Draw the diagram.}$ $\text{The diagram shows a pendulum with positions A, B, and C, where B is the equilibrium position and A and C are the extreme positions.}$ $\text{Step 2: Analyze the forces at each position.}$ $\text{The velocities at extreme positions A and C are zero. So there is only tangential force and no centripetal force. At B, it has centripetal force due to velocity at the mean position.}$ $\text{At positions A and C (extreme positions):}$ $\text{- Velocity } v = 0$ $\text{- Only tangential component of weight acts: } mg\cos\theta$ $\text{- This tangential force points toward the equilibrium position B}$ $\text{- No centripetal force since velocity is zero}$ $\text{At position B (equilibrium/mean position):}$ $\text{- Velocity is maximum}$ $\text{- Net force has two components:}$ $\text{1. Tangential component = 0 (since it's at equilibrium)}$ $\text{2. Centripetal component points toward the center (upward along the string)}$ $\text{Therefore, the correct answer shows forces at A and C pointing toward B (restoring force), and the force at B pointing upward (centripetal force).}$
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