Check the dimensional consistency of P=hpg, where P is pressure, h is planck's constant, p is density and g is - Physics - Units And Measurements

Question

Check the dimensional consistency of P=hpg, where P is pressure, h
is planck's constant, p is density and g is accelaraion due to
gravity

Vaibhav T. · Accepted Answer

Dear Student,

P=hρgwhere P=pressureh=planck's constant=M1L2T-1ρ=density=M1L-3T0g=acceleration due to gravity=M0L1T-2P=M1L2T-1M1L-3T0M0L1T-2P=M1+1+0L2-3+1T-1+0-2P=M2L0T-3But we know that dimensional formual of Pressure=M1L-1T-2Hence, the formula is incorrect

Check the dimensional consistency of P=hpg, where P is pressure, h is planck's constant, p is density and g is accelaraion due to gravity.