Question

Which of the following do not have the same dimensions as the other three?

Given that: $l=$ length, $m=$ mass, $k=$ force constant, $I=$momet of inertia, $B=$ magnetic induction, $P_m=$ magnetic dipole moment, $R=$ radius and $g=$ acceleration due to gravity

• A. $\sqrt{\frac{l}{g}}$
• B. $\sqrt{\frac{I}{P_{m}B}}$
• C. $\sqrt{\frac{k}{m}}$
• D. $\sqrt{\frac{R}{g}}$

Answer 1

The correct option is C $\sqrt{\frac{k}{m}}$

$\sqrt{\frac{l}{g}}=\sqrt{\frac{L^1}{L^1{T}^{-2}}}=P^1$
$\sqrt{\frac{I}{P_{m}B}}=\sqrt{\frac{M^1{L}^2}{M^1{L}^2{T}^{-2}}}=P^1$
$\sqrt{\frac{k}{m}}=\sqrt{\frac{M^1{T}^{-2}}{M^1}}=P^{-1}$
$\sqrt{\frac{R}{g}}=\sqrt{\frac{L^1}{L^1{T}^{-2}}}=P^1$
Hence, option C is correct.