According to the law of conservation of energy, in an isolated system:
A. Potential energy remains constant
B. Total mechanical energy remains constant if only conservative forces act
C. Thermal energy is always zero
D. Kinetic energy remains constant
Answer: Option B
Solution (By JKSSB Mock Tests)
Law of conservation of energy states total energy (all forms) is conserved in isolated systems. For mechanical energy (KE + PE) to be conserved, only conservative forces (like gravity, spring) must act; non-conservative forces (friction) convert mechanical energy to heat. Option C precisely states this condition. Options A and B are incorrect as KE and PE individually vary. Option D is false as thermal energy can exist. Memory tip: 'Mechanical energy conserved ⇔ no non-conservative work'. This nuanced understanding is critical for energy problems in competitive exams, where distractors often omit the conservative force condition.
Explanation:
Orbital velocity v = √(GM/r), where r is orbital radius from Earth's center. Thus v ∝ 1/√r. If r increases, v decreases. This follows from equating gravitational force to centripetal force: GMm/r² = mv²/r ⇒ v = √(GM/r). Higher orbits have slower speeds but longer periods. Memory aid: 'Higher orbit, slower speed' – counterintuitive but fundamental. This relationship is crucial for satellite motion questions in competitive exams. Always distinguish orbital velocity from escape velocity (which is √2 times orbital velocity at same radius).
Explanation:
Distance covered in nth second: sₙ = u + a(2n-1)/2. With u=0, sₙ ∝ (2n-1). For n=1: 2(1)-1=1; n=2: 3; n=3:5. Thus ratio 1:3:5. This result holds for any uniformly accelerated motion starting from rest. The distances covered in successive equal time intervals follow odd number ratio. Memory aid: This is a standard result derivable from s = ut + ½at² by calculating s at t=n and t=n-1. Frequently appears in competitive exams testing equation of motion applications.
Explanation:
At 0°C, speed ~ 331 m/s. At room temperature (20°C) ~ 343 m/s, often taken as 340. Increases with temperature v ∝ √T. For many problems 340 is used, but at 0°C it's 331. So option A.
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