Question

Convert 10 Joule into erg with the help of dimensional analysis.​

Answer 1

$\maltese\:\underline{\textsf{\textbf{AnsWer :}}}\:\maltese$

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We know that,

$\longrightarrow\:\:\sf 1 \: J = 1 \: kg. m^2 .s^{-2}$

$\footnotesize \bullet \: \underline{\:\rm Dimensions \: of \: 1 \: kg. m^2 .s^{-2} = [M L^2 T^{-2}]}$

$\longrightarrow\:\:\sf n_1u_1 = n_2 u_2$

$\longrightarrow\:\:\sf n_2 =n_1 \Bigg[\dfrac{u_1}{u_2} \Bigg]$

$\longrightarrow\:\:\sf n_2 =1\Bigg[\dfrac{M_1}{M_2} \Bigg]^{1} \Bigg[\dfrac{L_1}{L_2} \Bigg]^{2}\Bigg[\dfrac{T_1}{T_2} \Bigg]^{ - 2}$

$\footnotesize \bullet \: \underline{\:\rm T_1 = T_2}$

$\longrightarrow\:\:\sf n_2 =1\Bigg[\dfrac{M_1}{M_2} \Bigg]^{1} \Bigg[\dfrac{L_1}{L_2} \Bigg]^{2}$

$\longrightarrow\:\:\sf n_2 =1\Bigg[\dfrac{1 \: kg}{g} \Bigg]^{1} \Bigg[\dfrac{1 \: m}{cm} \Bigg]^{2}$

$\footnotesize \bullet \: \underline{\:\rm 1 \: kg = 1000 \: g}$

$\footnotesize \bullet \: \underline{\:\rm 1 \: m = 100 \: cm \: }$

$\longrightarrow\:\:\sf n_2 =1\Bigg[\dfrac{1000 \: g}{g} \Bigg]^{1} \Bigg[\dfrac{100 \: cm }{cm} \Bigg]^{2}$

$\longrightarrow\:\:\sf n_2 =1\Bigg[1000 \Bigg]^{1} \Bigg[100 \Bigg]^{2}$

$\longrightarrow\:\:\sf n_2 =1\Bigg[1000 \Bigg] \Bigg[100 00 \Bigg]$

$\longrightarrow\:\:\sf n_2 = {10}^{7}$

$\longrightarrow\:\: \underline{ \underline{\sf 1 \: J = {10}^{7} \: erg}}$

$\longrightarrow\:\: \underline{ \underline{\sf 1 0 \: J = 10 \times {10}^{7} \: erg}}$

$\longrightarrow\:\: \underline{ \underline{\sf 1 0 \: J = {10}^{8} \: erg}}$

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