The moment of inertia of HCl molecule about an axis passing through its centre o

Question

The moment of inertia of HCl molecule about an axis passing through its centre of mass and perpendicular to the line joining the

H^{+}

and

C l^{-}

ions will be, if the interatomic distance is 1

o A

Options:

A . 0.61×10−47kg.m2

B . 1.61×10−47kg.m2

C . 0.061×10−47kg.m2

D . 0

Answer: Option B
:
B
If

r_{1}

and

r_{2}

are the respective distances of particles

m_{1}

and

m_{2}

from the centre of mass then

m_{1} r_{1} = m_{2} r_{2} \Rightarrow 1 \times x = 35.5 \times (L - x) \Rightarrow x = 35.5 (1 - x)

\Rightarrow x = 0.973 o A

and

L - x = 0.027 o A

Moment of inertia of the system about centre of mass

I = m_{x}^{2} + m_{2} (L - x)^{2}

I = 1 a m u \times (0.973 o A)^{2} + 35.5 a m u \times (0.027 o A)^{2}

Substituting 1 a.m.u.

= 1.67 \times 10^{- 27} k g

and

1 o A = 10^{- 10} m

I = 1.62 \times 10^{- 47} k g m^{2}

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