TS EAMCET 20-July-2022 Shift 1 Solved Paper

Velocity of light, [c]=[LT−1]
Gravitational constant,
[G]=[M−1L3T−2]
Planck's constant, [h]=[ML2T−1]
Let dimensions of density d in new system are
d=ca,Gb,hc
Then expressing both sides in terms of dimensions of fundamental units, we get
‌‌[ML−3]=[LT−1]a[M−1L3T−2]b[ML2T−1]c
⇒‌‌[ML−3]=[M−b+cLa+3b+2cT−a−2b−c]
Comparing both sides we get,
−b+c=1....(i)
a+3b+2c=−3...(ii)
and −a−2b−c=0...(iii)
Solving these we get,
a=5,b=−2,c=−1
So, density can be expressed as
d=c5G−2h−1