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JEE Main 2018 (15 Apr, Shift 2) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2018 (15 Apr, Shift 2)

Q63JEE Main 2018 · 15 APR · SHIFT 2Medium

Applications of Dimensional Analysis

The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives the Planck length?

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Answer: (d)

$[G\hbar] = M^{-1}L^3T^{-2}\cdot ML^2T^{-1} = L^5T^{-3}$ .
Dividing by $[c^3] = L^3T^{-3}$ gives $L^2$ .
$\left(\dfrac{G\hbar}{c^3}\right)^{1/2}$ has dimension $L$ .
So the answer is (d).

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