A Long Thin Rod Has Its One End at X $\lambda$

question 58

Multiple Choice

A long thin rod has its one end at x = 0 and the other end at x =1 m.Its composition is such that the linear mass density changes with length according to $\lambda$ (x) = ax² + bx+c,where x is the distance from one end of the rod.Given: a = 0.75 kg/m³,b = 0.5 kg/m²,and c = .25 kg/m,the center of mass of the rod relative to x = 0 is

• A)0.41 m.
• B)0.52 m.
• C)0.60 m.
• D)0.64 m.

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Definitions:

Paradoxical Sleep

Another term for REM (Rapid Eye Movement) sleep, characterized by active brain patterns, dream occurrence, and temporary muscle paralysis.

Very Relaxed Muscles

A state of low tension in muscle fibers, often achieved through relaxation techniques, leading to reduced physical stress and strain.

Sleep Patterns

The natural cycle of various stages of sleep including REM and non-REM stages that repeats throughout the night.

Genetically Influenced

Traits or conditions that are shaped in part by genes inherited from one's parents.