Question

Convert 76 cm of mercury pressure into Nm−2 using the method of dimensions​

Answer 1

Answer:

Convert 76cm of mercury pressure into Nm^(-2) using the method of dimensions. So a=1,b=-1,c=-2. P2=1.01×105Nm-2.

Answer 2

To prove:

p2=1.01×10^5Nm^-2

Proof:

In cgs system 76cm of mercury pressure=76×13.6×980dyne cm-2

The dimensional formula of pressure is [ML^-1T^-2]

p1[M1^aL1^bT1^c]=p2[M2^aL2^bT2^c]

p2=p1[M1/M2]^a [L1/L2]^b [T1/T2]^c

M1=1g,M2=1kg

L1=1cm,L2=1m

T1=1s,T2=1s

if a=1,b=-1,c=-2

then,

p2=76×13.6×980[1g/1kg]^1 [1cm/1m]^-1 [1s/1s]^-2

=76×13.6×980[10^-3kg/1kg]^1 [10^-2m/1m]^-1 [1s/1s]^-2

=76×13.6×980×10^-3 ×10^2

p2=1.01×10^5Nm^-2