A) \[(1\sqrt{2})a\]
B) \[(\sqrt{3/2})a\]
C) \[(\sqrt{2/3})a\]
D) \[(\sqrt{1/3})a\]
Correct Answer: C
Solution :
[c] The equation of a semi - circular wave is \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] or \[{{y}^{2}}={{a}^{2}}-{{x}^{2}}\] \[{{I}_{rms}}=\sqrt{\frac{1}{2a}\int_{-a}^{+a}{{{y}^{2}}dx}}\] \[{{I}^{2}}_{rms}=\frac{1}{2a}\int_{-a}^{+a}{({{a}^{2}}-{{x}^{2}})dx}\] \[=\frac{1}{2a}\int_{-a}^{+a}{({{a}^{2}}-{{x}^{2}}})dx=\frac{1}{2a}\left| a\left. ^{2}x-\frac{{{x}^{3}}}{3} \right| \right._{-a}^{+a}\] \[=\frac{1}{2a}\left( {{a}^{3}}-\frac{{{a}^{3}}}{3}+{{a}^{3}}-\frac{{{a}^{3}}}{3} \right)=\frac{2{{a}^{2}}}{3}\] \[{{I}_{rms}}=\sqrt{\frac{2{{a}^{2}}}{3}}=\sqrt{\frac{2}{3}}a\]
You need to login to perform this action.
You will be redirected in
3 sec
