The root mean square speed of gas molecules is proportional to:
A. Temperature
B. Square root of temperature
C. Square of temperature
D. Inverse of temperature
Answer: Option B
Solution (By JKSSB Mock Tests)
From kinetic theory, rms speed v_rms = √(3RT/M), where R is gas constant, T absolute temperature, M molar mass. Thus v_rms ∝ √T. This shows molecular speed increases with temperature but not linearly. Memory aid: 'Kinetic energy ∝ T; KE = ½mv² ⇒ v ∝ √T'. This conceptual question tests kinetic theory understanding, frequently examined in thermodynamics sections of competitive exams. Always use absolute temperature (Kelvin) in gas law calculations; Celsius would give incorrect proportionality.
Explanation:
Coulomb's law: E = kq/r² ⇒ E ∝ 1/r². Inverse square law fundamental to electrostatics and gravitation. Memory tip: 'Point charge field: inverse square; double distance ⇒ field becomes 1/4'. Electrostatics concept frequently tested in competitive exams.
Explanation:
Vector equilibrium: three equal forces at 120° form closed triangle. Third force equals magnitude of others, oriented 120° from each. Memory aid: 'Equilibrium: vector sum = 0; symmetric forces ⇒ symmetric angles'. Statics concept frequently tested in competitive exams.
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