Simple harmonic motion is characterized by: MCQ with Answer and Explanation

Question
Simple harmonic motion is characterized by:
A. Acceleration proportional to velocity
B. Constant acceleration
C. Constant velocity
D. Acceleration proportional to displacement and directed opposite
Answer: Option D
Solution (By JKSSB Mock Tests)
SHM definition: acceleration a ∝ -x (displacement), i.e., a = -ω²x. This restoring acceleration causes oscillatory motion. Constant acceleration implies uniformly accelerated motion (not oscillatory). Constant velocity implies no acceleration. Memory tip: 'SHM: a = -ω²x; force F = -kx (Hooke's law)'. This conceptual question tests fundamental SHM characteristics, frequently examined in competitive exams. Always link to examples: mass-spring system, simple pendulum (small angles), LC circuits.
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Question #1
The escape velocity from Earth does not depend on
A. Mass of Earth
B. Universal gravitational constant
C. Mass of the object
D. Radius of Earth
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Correct Answer: Option C

Explanation:
v_esc = √(2GM/R), independent of m. Heavier object needs more energy, but velocity same. All objects fall at same rate. Important concept.
This question belongs to: Science Physics
Question #2
If the momentum of a body is increased by 100%, its kinetic energy increases by
A. 200%
B. 400%
C. 300%
D. 100%
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Correct Answer: Option C

Explanation:
Kinetic energy K = p²/(2m). If p becomes 2p (100% increase), K' = (2p)²/(2m) = 4p²/(2m) = 4K. So increase = 4K - K = 3K, i.e., 300% increase. Common mistake: think linear. Remember quadratic relationship. Percent increase = (new-old)/old × 100% = (4K-K)/K ×100 = 300%.
This question belongs to: Science Physics
Question #3
The time taken for a ball dropped from height h to reach ground is t. If dropped from height 4h, the time taken is:
A. t/2
B. 2t
C. 4t
D. t
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Correct Answer: Option B

Explanation:
Free fall: h = ½gt² ⇒ t = √(2h/g). Thus t ∝ √h. If h' = 4h, t' = √(4h/g) = 2√(h/g) = 2t. Time doubles when height quadruples. Memory aid: 'Free fall time: t ∝ √h; quadruple height ⇒ double time'. This kinematics proportional reasoning problem is frequently tested in competitive exams. Always derive the proportionality from fundamental equations; avoid assuming linear relationships for non-linear motion.
This question belongs to: Science Physics
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