विमीय विश्लेषण – समस्याएं और समाधान
1. विमीय विश्लेषण के आधार पर, निम्नलिखित भौतिक आयामों का निर्धारण करें जिनके आयाम समान हों।
बी. शक्ति और दबाव
सी. बल और संवेग
डी. कार्य और ऊष्मा
ज्ञात :
Dimension of length = dimension of width = dimension of displacement = L
Dimension of time = T
Dimension of mass = M
समाधान:
Dimension of area = लंबाई का आयाम x dimension of width = [L][L] = [L]2
Dimension of velocity = का आयाम विस्थापन / dimension of time = [L] / [T] = [L][T]-1
Dimension of acceleration = dimension of velocity / dimension of time = [L][T]-1 / [T] = [L][T]-1[टी]-1 = [L][T]-2
Dimension of force = dimension of mass x dimension of acceleration = [M][L][T]-2
Dimension of work = dimension of force x dimension of displacement = [M][L][T]-2 [एल] = [एम][एल]2[टी]-2
Dimension of power = dimension of work / dimension of time = [एम][एल]2[टी]-2 / [टी] = [एम][एल]2[टी]-2[टी]-1 = [एम][एल]2[टी]-3
के आयाम दबाव = dimension of force / dimension of area = [M][L][T]-2 / [एल]2 = [M][L][T]-2 [एल]-2 = [एम] [एल]-1[टी]-2
आयाम of momentum = dimension of mass x dimension of velocity = [M][L][T]-1
Dimension of heat = dimension of energy = dimension of work = [एम][एल]2[टी]-2
सही उत्तर है D.
नोट:
गर्मी is energy that moves due to the temperature difference.
Work is the process of energy transfer through the displacement of objects.
So, the dimension of heat = the dimension of energy = the dimension of work.
2. Two quantities that have the same quantity but have a different physical concept…
A. Force and momentum
B. Energy and force
C. Potential energy and kinetic energy
D. Energy and momentum
समाधान:
Unit of potential energy = unit of गतिज ऊर्जा = unit of energy = unit of work.
Although it has the same unit, but the potential energy and the kinetic energy are different types of energy.
सही जवाब सी है।
3. The following quantities that have the same units are…
A. Force and emf
B. Velocity and acceleration
C. कार्य और ऊर्जा
D. Work and power
समाधान:
Work is the process of energy transfer through the displacement of objects.
Energy is the ability to do work.
Work and energy are two quantities of physics that have the same unit.
सही जवाब सी है।
