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STATEMENT-1 : In simple pendulum perform...

STATEMENT-1 : In simple pendulum performing `S.H.M`., net acceleration is always between tangential and radial acceleration except at lowest point.
STATEMETN-2 : At lowest point tangential acceleration is zero.

A

(a)Statement I is true statement II is true, Statement II is a correct explanation for Statement I.

B

(b)Statement I is true statement II is true, Statement II is NOT a correct explanation for Statement I.

C

(c)Statement I is true, Statement II is false

D

(d)Statement I is false, Statement II is true

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze both statements given in the question regarding the simple harmonic motion (SHM) of a simple pendulum. ### Step-by-Step Solution: **Step 1: Understanding Statement 1** - Statement 1 claims that in a simple pendulum performing SHM, the net acceleration is always between the tangential and radial (centripetal) acceleration except at the lowest point. - In SHM, the pendulum experiences two components of acceleration: - **Tangential Acceleration (a_t)**: This is due to the component of gravitational force acting along the direction of motion (mg sin θ). - **Radial Acceleration (a_r)**: This is due to the tension in the string and the component of gravitational force acting perpendicular to the direction of motion (mg cos θ). - The net acceleration (a_net) is a vector sum of these two components. At any point other than the lowest point, the net acceleration will indeed lie between these two components. **Conclusion for Statement 1**: True. **Step 2: Understanding Statement 2** - Statement 2 states that at the lowest point, the tangential acceleration is zero. - At the lowest point of the pendulum's swing (when θ = 0), the motion is purely horizontal, and the gravitational force acts vertically downward. - Since tangential acceleration is given by a_t = g sin θ, at θ = 0, sin(0) = 0, which means: - **Tangential Acceleration (a_t)** = 0. **Conclusion for Statement 2**: True. **Step 3: Evaluating the Relationship Between the Statements** - Both statements are true, but they describe different aspects of the motion of the pendulum. - Statement 1 discusses the relationship between net acceleration and its components throughout the motion, while Statement 2 specifically addresses the condition at the lowest point. ### Final Conclusion: Both Statement 1 and Statement 2 are true, but they are not directly explaining each other. Therefore, the correct answer is that both statements are true, but Statement 2 does not provide a correct explanation for Statement 1. ### Answer: Option B (Both statements are true, but Statement 2 is not a correct explanation for Statement 1). ---

To solve the problem, we need to analyze both statements given in the question regarding the simple harmonic motion (SHM) of a simple pendulum. ### Step-by-Step Solution: **Step 1: Understanding Statement 1** - Statement 1 claims that in a simple pendulum performing SHM, the net acceleration is always between the tangential and radial (centripetal) acceleration except at the lowest point. - In SHM, the pendulum experiences two components of acceleration: - **Tangential Acceleration (a_t)**: This is due to the component of gravitational force acting along the direction of motion (mg sin θ). ...
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