Answer

Verified

348k+ views

**Hint:**When a body is in translational motion it moves with a linear acceleration while body rotates due to torque acting on it it produce an angular acceleration and the relation between torque and moment of inertia is related as $\vec \tau = I\vec \alpha $.

**Complete step by step answer:**

Let us assume that $I$ is the moment of inertia of the body and it’s given that:

The magnitude of angular acceleration of the body is $\alpha = 20\,rad\,{\sec ^{ - 2}}$.

The magnitude of torque acting on the body is $\tau = 400Nm$.

The mass of the given body is $m = 40\,Kg$.

Now, using the relation $\vec \tau = I\vec \alpha $ we get,

$400 = I \times 20$

$\therefore I = 20\,Kg{m^2}$

So, the moment of inertia of the body is $I = 20\,Kg{m^2}$.

Now, as we know that the general formula of Moment of inertia is written as,

$I = M{K^2}$

where $K$ denotes the radius of gyration

Now we have, the magnitude of moment of inertia is $I = 20\,Kg{m^2}$

Mass of the body is $m = 40\,Kg$

Putting these value in equation $I = M{K^2}$

We get,

$20 = 40 \times {K^2}$

$\Rightarrow K = \dfrac{1}{{\sqrt 2 }}$

$\therefore K = 0.707\,m$

So, the radius of gyration of the body is $K = 0.707m$

**Hence, the moment of inertia of the body is $I = 20\,Kg\,{m^2}$ and the radius of gyration of the body is $K = 0.707\,m$.**

**Note:**It should be remembered that, the radius of gyration of the body is the distance from the body to the axis of rotation which have same moment of inertia if whole mass of body considered to be act at that particular point and produce same moment of inertia with particular distance, this radius is called radius of gyration.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE