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The speed of light,gravitational constant,planks constant are taken as fundamental units in a system.The dimensions of the time in the new

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speed of light=m/s
gravitational constant(G)=Nm^2/kg^2=kg(m/s^2)(m^2/kg^2)=m^3/kgs^2
plank's constant(P)=Js=kg(m/s^2)(m)(s)=kgm^2/s
            time(t)=(c)^x(G)^y(P)^z
                              =(m/s)^x(m^3/kgs^2)^y(kgm^2/s)^z
                              =(m)^x^+^3^y^+^2^z(kg)^-^y^+^z(s)^-^x^-^y^2^-^z
                         Thus,
                                       x+3y+2z=0
                                       -y+z=0
                                        -x-y^2-z=0
                        from these equations, we find
                                                    y=z=-6(z\neq 0)
                                                    x=-5z=(-5)(-6)=30
                                       Hence answer is (c)^3^0(G)^-^6(P)^-^6

Posted by

Harsh

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speed of light=m/s
gravitational constant(G)=Nm^2/kg^2=kg(m/s^2)(m^2/kg^2)=m^3/kgs^2
plank's constant(P)=Js=kg(m/s^2)(m)(s)=kgm^2/s
            time(t)=(c)^x(G)^y(P)^z
                              =(m/s)^x(m^3/kgs^2)^y(kgm^2/s)^z
                              =(m)^x^+^3^y^+^2^z(kg)^-^y^+^z(s)^-^x^-^y^2^-^z
                         Thus,
                                       x+3y+2z=0
                                       -y+z=0
                                        -x-y^2-z=0
                        from these equations, we find
                                                    y=z=-6(z\neq 0)
                                                    x=-5z=(-5)(-6)=30
                                       Hence answer is (c)^3^0(G)^-^6(P)^-^6

Posted by

Rakesh

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