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1
PhysicsMediumMCQAIIMS · 1986
$8\, cm$ લાંબી અને $1.5\, kg/m^3$ ઘનતા ધરાવતી રબરની દોરીનો યંગ મોડ્યુલસ $5 \times 10^8\, N/m^2$ છે. જો તેને રૂમમાં છત પરથી લટકાવવામાં આવે,તો તેના પોતાના વજનને કારણે લંબાઈમાં થતો વધારો કેટલો હશે?
A
$9.6 \times 10^{-5}\, m$
B
$9.6 \times 10^{-11}\, m$
C
$9.6 \times 10^{-3}\, m$
D
$9.6\, m$
Solution
(B) દોરીની લંબાઈ $L$,ઘનતા $d$ અને યંગ મોડ્યુલસ $Y$ હોય,તો તેના પોતાના વજનને કારણે થતો વધારો $\Delta L = \frac{L^2 dg}{2Y}$ સૂત્ર દ્વારા મળે છે.
આપેલ કિંમતો: $L = 8\, cm = 8 \times 10^{-2}\, m$,$d = 1.5\, kg/m^3$,$Y = 5 \times 10^8\, N/m^2$,અને $g = 9.8\, m/s^2$.
સૂત્રમાં કિંમતો મુકતા:
$\Delta L = \frac{(8 \times 10^{-2})^2 \times 1.5 \times 9.8}{2 \times 5 \times 10^8}$
$\Delta L = \frac{64 \times 10^{-4} \times 14.7}{10^9}$
$\Delta L = \frac{940.8 \times 10^{-4}}{10^9} = 9.408 \times 10^{-11}\, m$.
આપેલા વિકલ્પો મુજબ નજીકની કિંમત $9.6 \times 10^{-11}\, m$ છે.
આપેલ કિંમતો: $L = 8\, cm = 8 \times 10^{-2}\, m$,$d = 1.5\, kg/m^3$,$Y = 5 \times 10^8\, N/m^2$,અને $g = 9.8\, m/s^2$.
સૂત્રમાં કિંમતો મુકતા:
$\Delta L = \frac{(8 \times 10^{-2})^2 \times 1.5 \times 9.8}{2 \times 5 \times 10^8}$
$\Delta L = \frac{64 \times 10^{-4} \times 14.7}{10^9}$
$\Delta L = \frac{940.8 \times 10^{-4}}{10^9} = 9.408 \times 10^{-11}\, m$.
આપેલા વિકલ્પો મુજબ નજીકની કિંમત $9.6 \times 10^{-11}\, m$ છે.
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