Q.

If volume is written as V=Kgxcyhz. Here, K is dimensionless constant and g, c, h are gravitational constant, speed of light and Planck's constant, respectively. Find the value of x/z.

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answer is 1.

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Detailed Solution

LHS=[L]3RHS=M−1L3T−2xLT−1yML2T−1z        =M−x+zL3x+y+2zT−2x−y−zAccording to homogeneity principle,LHS = RHS∵   −x+z=0∴   z=x                      .........(i)        3x+y+2z=3        5x+y=3             ..........(ii)and  −2x−y−z=0 or −2x−y−x=0or     −3x−y=0  or     3x+y=0            ...........(iii)From Eqs. (ii) and (iii), we get        2x=3⇒x=3/2∴ z=x=3/2⇒3x+y=0 or  92+y=0⇒y=−92∴ xz=3/23/2=1
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