Young's modulus \(Y =\frac{\text { stress }}{\text { strain }}\) Dimension of \(Y =\frac{ M L ^{-1} T ^{-2}}{ M ^{0} L ^{0} T ^{0}}\)\(=\left[ M L ^{-1} T ^{-2}\right]\)
02. UNITS AND MEASUREMENTS (HM)
204783
यदि आवृत्ति, घनत्व \((\rho )\) लंबाई \((a)\) तथा पृष्ठ-तनाव \((T)\) का फलन हो तो इसका मान होगा
1 \(k\,{\rho ^{1/2}}{a^{3/2}}/\sqrt T \)
2 \(k\,{\rho ^{3/2}}{a^{3/2}}/\sqrt T \)
3 \(k\,{\rho ^{1/2}}{a^{3/2}}/{T^{3/4}}\)
4 \(k\,{\rho ^{1/2}}{a^{1/2}}/{T^{3/2}}\)
Explanation:
(a) माना \(n = k{\rho ^a}{a^b}{T^c}\) जहाँ \([\rho ] = [M{L^{ - 3}}],\;[a] = [L]\) तथा \([T] = [M{T^{ - 2}}]\) दोनों ओर विमाओं की तुलना करने पर \(a = \frac{1}{2},\,b = \frac{3}{2}\) तथा \(c = \frac{{ - 1}}{2}\) $⇒$ \(\eta = \frac{{k{\rho ^{1/2}}{a^{3/2}}}}{{\sqrt T }}\)
Young's modulus \(Y =\frac{\text { stress }}{\text { strain }}\) Dimension of \(Y =\frac{ M L ^{-1} T ^{-2}}{ M ^{0} L ^{0} T ^{0}}\)\(=\left[ M L ^{-1} T ^{-2}\right]\)
02. UNITS AND MEASUREMENTS (HM)
204783
यदि आवृत्ति, घनत्व \((\rho )\) लंबाई \((a)\) तथा पृष्ठ-तनाव \((T)\) का फलन हो तो इसका मान होगा
1 \(k\,{\rho ^{1/2}}{a^{3/2}}/\sqrt T \)
2 \(k\,{\rho ^{3/2}}{a^{3/2}}/\sqrt T \)
3 \(k\,{\rho ^{1/2}}{a^{3/2}}/{T^{3/4}}\)
4 \(k\,{\rho ^{1/2}}{a^{1/2}}/{T^{3/2}}\)
Explanation:
(a) माना \(n = k{\rho ^a}{a^b}{T^c}\) जहाँ \([\rho ] = [M{L^{ - 3}}],\;[a] = [L]\) तथा \([T] = [M{T^{ - 2}}]\) दोनों ओर विमाओं की तुलना करने पर \(a = \frac{1}{2},\,b = \frac{3}{2}\) तथा \(c = \frac{{ - 1}}{2}\) $⇒$ \(\eta = \frac{{k{\rho ^{1/2}}{a^{3/2}}}}{{\sqrt T }}\)
Young's modulus \(Y =\frac{\text { stress }}{\text { strain }}\) Dimension of \(Y =\frac{ M L ^{-1} T ^{-2}}{ M ^{0} L ^{0} T ^{0}}\)\(=\left[ M L ^{-1} T ^{-2}\right]\)
02. UNITS AND MEASUREMENTS (HM)
204783
यदि आवृत्ति, घनत्व \((\rho )\) लंबाई \((a)\) तथा पृष्ठ-तनाव \((T)\) का फलन हो तो इसका मान होगा
1 \(k\,{\rho ^{1/2}}{a^{3/2}}/\sqrt T \)
2 \(k\,{\rho ^{3/2}}{a^{3/2}}/\sqrt T \)
3 \(k\,{\rho ^{1/2}}{a^{3/2}}/{T^{3/4}}\)
4 \(k\,{\rho ^{1/2}}{a^{1/2}}/{T^{3/2}}\)
Explanation:
(a) माना \(n = k{\rho ^a}{a^b}{T^c}\) जहाँ \([\rho ] = [M{L^{ - 3}}],\;[a] = [L]\) तथा \([T] = [M{T^{ - 2}}]\) दोनों ओर विमाओं की तुलना करने पर \(a = \frac{1}{2},\,b = \frac{3}{2}\) तथा \(c = \frac{{ - 1}}{2}\) $⇒$ \(\eta = \frac{{k{\rho ^{1/2}}{a^{3/2}}}}{{\sqrt T }}\)
Young's modulus \(Y =\frac{\text { stress }}{\text { strain }}\) Dimension of \(Y =\frac{ M L ^{-1} T ^{-2}}{ M ^{0} L ^{0} T ^{0}}\)\(=\left[ M L ^{-1} T ^{-2}\right]\)
02. UNITS AND MEASUREMENTS (HM)
204783
यदि आवृत्ति, घनत्व \((\rho )\) लंबाई \((a)\) तथा पृष्ठ-तनाव \((T)\) का फलन हो तो इसका मान होगा
1 \(k\,{\rho ^{1/2}}{a^{3/2}}/\sqrt T \)
2 \(k\,{\rho ^{3/2}}{a^{3/2}}/\sqrt T \)
3 \(k\,{\rho ^{1/2}}{a^{3/2}}/{T^{3/4}}\)
4 \(k\,{\rho ^{1/2}}{a^{1/2}}/{T^{3/2}}\)
Explanation:
(a) माना \(n = k{\rho ^a}{a^b}{T^c}\) जहाँ \([\rho ] = [M{L^{ - 3}}],\;[a] = [L]\) तथा \([T] = [M{T^{ - 2}}]\) दोनों ओर विमाओं की तुलना करने पर \(a = \frac{1}{2},\,b = \frac{3}{2}\) तथा \(c = \frac{{ - 1}}{2}\) $⇒$ \(\eta = \frac{{k{\rho ^{1/2}}{a^{3/2}}}}{{\sqrt T }}\)
