Question

The dimensional formula of radius of gyration is:
A. $\left[ {{M^0}{L^0}{T^0}} \right]$
B. $\left[ {{M^0}{L^0}T} \right]$
C. $\left[ {{M^0}L{T^0}} \right]$
D. None of these.

Answer 1

Hint: Radius of gyration- it is the distance from an axis of the body at which the whole mass of the body may be assumed it be concentrated and at which the moment of inertia of that particular object will be equal moment of inertia of the actual mass about the axis, equals to the square root of the quotient of the moment of inertia and the mass. That is, $r = \sqrt {\dfrac{I}{A}} $.

Complete answer:
From the definition of the radius of gyration we have come to know that, basically the radius of gyration is the measurement of the distance so the unit of the radius of gyration will be the same as that of the distance and the unit of the distance is metre. Hence the unit of the radius of gyration will be metre ($m$).

And the dimension of the metre is $\left[ L \right]$. So, the dimensional formula will contain only the dimension of the length and the other dimension of the other two fundamental units that are mass and time, will be zero.
So finally, the dimensional formula of the radius of gyration will be written as: $\left[ {{M^0}L{T^0}} \right]$.
The power of zero on the dimension of the mass and time shows that the mass and the time dimensions are zero for the radius of gyration.

So, the correct answer is “Option C”.

Note:
Use of the radius of gyration- radius of gyration is used to compare the different structural shapes when they are subjected to the compression along an axis. For a compression beam or the compression member the radius of gyration is used to predict the buckling of that particular compression member.