The work done by a conservative force in moving a particle along a closed path is:
A. Zero
B. Depends on path
C. Negative
D. Positive
Answer: Option A
Solution (By JKSSB Mock Tests)
Conservative forces (gravity, spring, electrostatic) have path-independent work; work done over any closed loop is zero. This defines conservative forces and enables potential energy definition. Non-conservative forces (friction) have non-zero closed-path work. Memory aid: 'Conservative force: ∮F·dr = 0; enables energy conservation'. This mechanics concept is frequently tested in competitive exams. Always link conservative forces to potential energy and mechanical energy conservation; this is foundational for advanced physics problem-solving.
Explanation:
Pressure has dimensions [ML⁻¹T⁻²]. Energy per unit volume: Energy is [ML²T⁻²], volume is [L³], so [ML²T⁻²]/[L³] = [ML⁻¹T⁻²], matching pressure. Force per unit length is [MLT⁻²]/[L] = [MT⁻²]. Momentum per unit area is [MLT⁻¹]/[L²] = [ML⁻¹T⁻¹]. Power per unit volume is [ML²T⁻³]/[L³] = [ML⁻¹T⁻³]. This dimensional equivalence explains why pressure appears in Bernoulli's equation alongside energy density. Memory aid: Pressure and energy density both represent stored energy per spatial dimension.
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