The time period of a simple pendulum is independent of:
A. Mass of bob
B. Amplitude (for small angles)
C. Acceleration due to gravity
D. Length of pendulum
Answer: Option A
Solution (By JKExamLibrary)
Pendulum period T = 2π√(l/g) for small amplitudes. It depends on length l and gravity g, but not on bob mass or amplitude (isochronism for small angles). Mass independence arises because gravitational force and inertia both proportional to mass, canceling out. Memory aid: 'Pendulum: T ∝ √(l/g); independent of mass and small-amplitude'. This conceptual question tests oscillations fundamentals, frequently examined in competitive exams. Always verify the small-angle approximation; competitive exams assume it unless specified otherwise. This problem assesses understanding of which parameters affect periodic motion.
Explanation:
Galileo Galilei conducted experiments rolling balls down inclined planes and concluded that an object in motion would continue moving indefinitely on a frictionless surface. This completely challenged Aristotelian mechanics and formulated the concept of inertia, which Isaac Newton later formalized as his First Law of Motion.
Explanation:
SONAR (Sound Navigation and Ranging) relies on the reflection of ultrasonic waves. A transmitter sends out sound waves, which travel through water, strike an object (like a submarine or the seabed), and reflect back as an echo to a receiver. By measuring the time taken for the echo to return, the distance can be calculated.
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