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Units and Measurements physics ncert solutions class 11th Physics Class 11th Physics NCERT Exemplar Solutions Class 11th Chapter Two

If Planck’s constant (h ) and speed of light in vacuum (c ) are taken as two fundamental quantities, which one of the following can, in addition, be taken to express length, mass and time in terms of the three chosen fundamental quantities?

(a) Mass of electron (m_e )

(b) Universal gravitational constant (G )

(c) Charge of electron

(d) Mass of proton (m_p)

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Answered by

Payal Gupta | Contributor-Level 10

3 months ago

This is a multiple choice answer as classified in NCERT Exemplar

(a,b,d) h=[ML²T^-1]

[c]=[LT^-1], [m_e]=M

[G]= [M^-1L³T^-2]

[e]=[AT],[m_p]=[M]

[ $\frac{h c}{G}$ ] = $\frac{[M L^{2} T^{- 1}] [L T^{- 1}]}{M^{- 1} L^{3} T^{- 2}} = M^{2}$

M= $\sqrt[]{\frac{h c}{G}}$

$\frac{h}{c} = \frac{M L^{2} T^{- 1}}{L T^{- 1}} = [M L]$

L= $\frac{h}{c M} = \frac{h}{c} \sqrt[]{\frac{G}{h c}} = \frac{\sqrt[]{G h}}{c^{3 / 2}}$

C= LT^-1

T= $\frac{[L]}{[C]}$ = $\frac{\sqrt[]{G h}}{c^{3 / 2} c} = \frac{\sqrt[]{G h}}{c^{5 / 2}}$

Hence a,b and d any can be used to express L,M and T in terms of three chosen fundamental quantities.

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