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If the velocity of light c, Planks constant, h and the gravitational constant G are taken as fundamental quantities, then express mass, length and time in terms of dimensions of these quantities.

Answer» <html><body><p></p>Solution :Here, `c=[LT^-1],h=[ML^2T^-1],`<br/>`G=[M^-1L^3T^-2]`<br/>`becauseE=hv,h=E/v,G=((Fd^2)/(m_1m_2))`<br/>Let `m=c^xh^yG^zto(1)`<br/>`implies[M^1L^0T^0]=(LT^-1)^x(ML^2T^-1)^y(M^-1L^3T^-2)^<a href="https://interviewquestions.tuteehub.com/tag/z-750254" style="font-weight:bold;" target="_blank" title="Click to know more about Z">Z</a>`<br/> `implies[M^1L^0T^0]=M^(y-z)L^(x+2y+2z)T^(-x-y-2z)`<br/>Applying the principle of homegenity of <a href="https://interviewquestions.tuteehub.com/tag/dimensions-439808" style="font-weight:bold;" target="_blank" title="Click to know more about DIMENSIONS">DIMENSIONS</a>, we get <br/> `y-z=1to(2),x+2y+3z=0to(3),`<br/> `-x-y-2z=0to(4)`<br/>Adding <a href="https://interviewquestions.tuteehub.com/tag/eq-446394" style="font-weight:bold;" target="_blank" title="Click to know more about EQ">EQ</a>.(2), eq.(3) and eq.(4). <br/> `2y=1impliesy=1/2` <br/> `therefore` From eq.(2) `z=y-1=1/2-1=(-1)/2`<br/>From eq.(4) `x=-y-2z=(-1)/2+1=1/2` <br/> Substituting the values of x,y &amp; z in eq.(1) , we get <br/> `m=c^(1//2)h^(1//2)G^(-1//2)impliesm=sqrt((<a href="https://interviewquestions.tuteehub.com/tag/ch-913588" style="font-weight:bold;" target="_blank" title="Click to know more about CH">CH</a>)/G)`<br/>Proceeding as above we can show that <br/> `L=sqrt((hG)/c^3)andT=sqrt((hG)/c^5)`</body></html>


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