Answer

Verified

348k+ views

**Hint:**In order to answer this question we first know about moment of inertia. Moment of inertia , is property of a body by morality of which it goes against any agency that endeavors to place it in motion or, in the event that it is moving, to adjust the direction of its speed.

**Complete step-by-step solution:**

Moment of inertia is known as the body opposing angular speed which is the result of mass of each molecule i.e. \[I=m{{r}^{2}}\] . Dimension of M.O.I. is \[\left[ {{M}^{1}}{{L}^{2}}{{T}^{0}} \right]\]

Let's draw a fig. to solve this problem quickly,

As , we know moment of inertia about any axis \[I=m{{r}^{2}}\]

From this above fig. we get \[\sin {{30}^{\circ }}=\dfrac{d}{1}\]

Now M.O.I. about axis \['1'\] \[\Rightarrow {{I}_{1}}=m{{\left( \dfrac{l}{2} \right)}^{2}}+m{{l}^{2}}\]

\[\Rightarrow {{I}_{1}}=\dfrac{m{{l}^{2}}}{4}+m{{l}^{2}}\]

\[\therefore {{I}_{1}}=\dfrac{5}{4}m{{l}^{2}}\]

And M.O.I about axis \['2'\] \[\Rightarrow {{I}_{2}}=m{{\left( \dfrac{\sqrt{3}l}{2} \right)}^{2}}\]

\[\Rightarrow {{I}_{2}}=\dfrac{3m{{l}^{2}}}{4}\]

Assume that the axis passing through the one corner and also perpendicular to plane \[\Rightarrow {{I}_{{}}}=m{{l}^{2}}+m{{l}^{2}}\]

\[\therefore I=2m{{l}^{2}}\]

**Therefore all of the above options are correct.**

**Note:**Moment of inertia comes from the Latin word “momentum” which simply means movement . Decreasing in rate of speed of rotation , is due to the increase of axis of rotation as the moment of inertia also increases.

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Guru Purnima speech in English in 100 words class 7 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

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

Difference Between Plant Cell and Animal Cell

Three liquids are given to you One is hydrochloric class 11 chemistry CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE