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1.Units, Dimensions and Measurement
hard
હાલના લંબાઇ,સમય અને દળ $(m, s, kg)$ ના એકમો $100\,m, 100\,s$ અને $\frac{1}{{10}}\,kg$ થાય તો
Aનવો વેગનો એકમ $10$ ગણો થાય.
Bનવો બળનો એકમ $\frac{1}{{1000}}$ ગણો થાય
Cનવો ઊર્જાંનો એકમ $10$ ગણો થાય
Dનવો દબાણનો એકમ $1000$ ગણો થાય
Solution
velocity $= m/sec ;$ in new system $= \frac{{100m}}{{100\sec }} = \frac{m}{{\sec }}$ (same)
force $ = \frac{{kg \times m}}{{{{\sec }^2}}}$; in new system $ = \frac{1}{{10}}kg \times \frac{{100m}}{{100\sec \, \times \,100\sec }}$ $ = \frac{1}{{1000}}\,\frac{{kg \times m}}{{{{\sec }^2}}}$
energy $ = \frac{{kg \times {m^2}}}{{{{\sec }^2}}}$ ; in new system $ = \frac{1}{{10}}kg \times \frac{{100m \times 100m}}{{100\sec \, \times \,100\sec }}$ $ = \frac{1}{{10}}\frac{{kg \times {m^{\rm{2}}}}}{{se{c^2}}}$
pressure $ = \frac{{kg}}{{m \times {{\sec }^2}}}$; in new system $ = \frac{1}{{10}}kg \times \frac{1}{{100}}m \times \frac{1}{{100\,sec \times 100\,sec}}$ $ = {10^{ – 7}}\frac{{kg}}{{m \times se{c^2}}}$
force $ = \frac{{kg \times m}}{{{{\sec }^2}}}$; in new system $ = \frac{1}{{10}}kg \times \frac{{100m}}{{100\sec \, \times \,100\sec }}$ $ = \frac{1}{{1000}}\,\frac{{kg \times m}}{{{{\sec }^2}}}$
energy $ = \frac{{kg \times {m^2}}}{{{{\sec }^2}}}$ ; in new system $ = \frac{1}{{10}}kg \times \frac{{100m \times 100m}}{{100\sec \, \times \,100\sec }}$ $ = \frac{1}{{10}}\frac{{kg \times {m^{\rm{2}}}}}{{se{c^2}}}$
pressure $ = \frac{{kg}}{{m \times {{\sec }^2}}}$; in new system $ = \frac{1}{{10}}kg \times \frac{1}{{100}}m \times \frac{1}{{100\,sec \times 100\,sec}}$ $ = {10^{ – 7}}\frac{{kg}}{{m \times se{c^2}}}$
Standard 11
Physics
