Q. No.1. \(u=\frac{e^2 h}{e a_0}\)
2. \(u=\frac{{e}^2 {c}}{h {a}_0}\)
3. \(u=\frac{h c}{e^2 a_0}\)
4. \(u=\frac{e^2a_0}{hc}\)
1. \({\left(\frac{h}{m e^2}\right)}\)
2. \({\left(\frac{hc}{m e^2}\right)}\)
3. \({\left(\frac{h}{c e^2}\right)}\)
4. \({\left(\frac{mc^2}{h e^2}\right)}\)
1. \({\eta\left(\frac{S \Delta \theta}{h}\right)\left(\frac{1}{\rho g}\right)}\)
2. \({\eta\left(\frac{S \Delta \theta}{\eta h}\right)\left(\frac{1}{\rho g}\right)}\)
3. \({S\Delta \theta\over \eta h}\)
4. \(\eta{S\Delta \theta\over h}\)
1. \([{M}]=[{T}^{-1}{C}^2 {h}] \)
2. \([{M}]=[{T}^{-1}{C}^{-2} {h}^{-1}]\)
3. \([{M}]=[{T}^{-1} {C}^{-2} {h}]\)
4. \([{M}]=[{T} ~{C}^{-2} {h}]\)
In SI units, the dimensions of \(\sqrt{\frac{\varepsilon_0}{\mu_0}} \) is:
1. \( A T^{-3} M L^{3 / 2} \)
2. \( A^{-1} T M L^3 \)
3. \( A T^2 M^{-1} L^{-1} \)
4. \( A^2 T^3 M^{-1} L^{-2}\)
If surface tension (\(S\)), Moment of Inertia (\(I\)) and Plank's constant (\(h\)), were to be taken as the fundamental units, the dimensional formula for linear momentum would be:
1. \( S^{3 / 2} I^{1 / 2} h^0 \)
2. \( S^{1 / 2} I^{1 / 2} h^{-1} \)
3. \( S^{1 / 2} I^{3 / 2} h^{-1} \)
4. \( S^{1 / 2} I^{1 / 2} h^0\)
In the formula \(X=5YZ^2\), \(X\) and \(Z\) have dimensions of capacitance and magnetic field, respectively. What are the dimensions of \(Y\) in SI units?
1. \(\left[M^{-3} L^{-2} T^8 A^4\right]\)
2. \(\left[M^{-2} L^{-2} T^6 A^3\right]\)
3. \(\left[M^{-1} L^{-2} T^4 A^2\right]\)
4. \(\left[M^{-2} L^0 T^{-4} A^{-2}\right]\)
Which of the following combinations has the dimension of electrical resistance (\(\varepsilon_0\) is the permittivity of the vacuum and \(\mu_0\) is the permeability of vacuum)?
1. \(\sqrt{\frac{\varepsilon_0}{\mu_0}}\)
2. \(\frac{\varepsilon_0}{\mu_0}\)
3. \(\frac{\mu_0}{\varepsilon_0}\)
4. \(\sqrt{\frac{\mu_0}{\varepsilon_0}}\)
1. \(\sqrt{ {hc}^5 \over {G}} \)
2. \(\sqrt{ {c}^3 \over {Gh}} \)
3. \(\sqrt{ {Gh} \over {c}^5} \)
4. \(\sqrt{ {Gh} \over {c}^3} \)
If speed \(v\), area \(A\) and force \(F\) are chosen as fundamental units, then the dimension of Young's modulus will be:
1. \(\left[FA^{-1} v^0 \right]\)
2. \(\left[FA^2 v^{-1} \right]\)
3. \( \left[FA^2 {v}^{-3}\right]\)
4. \(\left[FA^2 v^{-2}\right] \)
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