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Question

The dimensions of gravitational constant G and the moment of inertia are, respectively


A

ML3T-2,ML2T0

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B

M-1L3T-2,ML2T0

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C

M-1L3T-2,M-1L2T

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D

ML3T-2,M-1L2T

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Solution

The correct option is B

M-1L3T-2,ML2T0


Step 1: Use the gravitational formula,

Know that the gravitational formula,

F=Gm1m2r2, where G=Gravitational Constant, m1&m2=mass of the first body and the mass of the second body, and r=distance between both bodies.

G=Fr2m1m2

The formula for the moment of inertia is,

I=mk2, where m=mass, and k=length.

Step 2: Calculate the dimensions of gravitational constant and moment of inertia,

For the dimension of force, we know that

ForceF=massm×accelerationa=MLT-2=MLT-2

The dimensional formula for gravitation will be

G=Fr2m1m2G=MLT-2L2MM=MLT-2L2M2=M-1L3T-2

Now find the dimensional formula of the inertia,

I=ML2=ML2

Therefore dimensions of gravitational constant G and the moment of inertia are, respectively,M-1L3T-2andML2T0.

Hence, the correct option is B.


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