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PhysicsMultiple correct+4 / -2Question 10 of 60

JEE Advanced 2015 · Paper 1, Physics question 10

Planck's constant hh, speed of light cc and gravitational constant GG are used to form a unit of length LL and a unit of mass MM. Then the correct option(s) is(are)

Choose one or more options
Answer and worked solution

Official answer: A, C, D

Dimensions. [h]=ML2T−1[h]=ML^2T^{-1}, [c]=LT−1[c]=LT^{-1} and [G]=M−1L3T−2[G]=M^{-1}L^3T^{-2}.

Planck mass and length.
M=hcG,L=hGc3.M=\sqrt{\frac{hc}G},\qquad L=\sqrt{\frac{hG}{c^3}}.

So M∝cM\propto\sqrt c (A true) and M∝G−1/2M\propto G^{-1/2} (B false). Also L∝hL\propto\sqrt h and L∝GL\propto\sqrt G (C and D true).

(A), (C), (D)

Topics:Dimensional analysis
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