Planck’s constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option is (are)

Question

Planck’s constant h, speed of light  c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option is (are)

Infinity Learn · Accepted Answer

Mass in terms of h , c , GM∝hacbGc⇒$$M1$$∝$$ML2T$$−$$1aLT$$−$$1bM$$−$$1L3T$$−$$2c$$⇒$$M1$$∝Ma−$$cL2a+b+3cT$$−a−b−$$2cComparing$$ powers,a−$$c=1$$→(1)2a+b+3c=0$$→$$(2)a+b+2c=0$$→$$(3)On$$ solving $$(1), (2), (3),  $$a=12$$,$$b=12$$,$$c=$$−$$12$$∴M∝c  only →A  is correctIn the same way  Length in terms of h , c , GL∝hacbGc⇒$$L1$$∝$$ML2T$$−$$1aLT$$−$$1bM$$−$$1L3T$$−$$2c$$⇒$$L1$$∝Ma−$$cL2a+b+3cT$$−a−b−$$2cComparing$$ powers,a−$$c=0$$→$$12a+b+3c=1$$→$$2a+b+2c=0$$→$$3After$$ Solving $$a=12$$ , $$b=$$−$$32$$ , $$c=12$$⇒L∝$$h12c$$−$$32G12L$$∝h,L∝G→C,D  are correct

Planck’s constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option is (are)

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