Answer
Verified
401.1k+ views
Hint: The term used in this question diagonal of cube means that it is the segment that joins the two points that are not the end points that are not the end point of the edge. But the main diagonal cube is the one that cuts through the centre of the cube.Try to find the relation between dimensions of cube and sphere and then proceed.
Step By Step Answer:
As we can see our cube diagonal is
$
\sqrt 3 a = 2R \\
\Rightarrow a = \dfrac{{2R}}{3} \\
$
As we say $ {M^ / } $is the mass of the cube so, material is same thus sphere density must equal to the cube density.
$
\dfrac{M}{{\dfrac{4}{3}\pi {R^3}}} = \dfrac{{{M^ / }}}{{{a^3}}} \\
\Rightarrow {M^ / } = \dfrac{{3M{a^3}}}{{4\pi {R^3}}}.......................................(a = 8) \\
\Rightarrow \dfrac{{3M}}{{4\pi {R^3}}} \times \dfrac{{8{R^3}}}{{3\sqrt 3 }} = \dfrac{{2M}}{{\sqrt 3 \pi }} \\
$
AS WE KNOW THAT MOMENT OF INERTIA IS:
$
I = \dfrac{1}{6}{M^ / }{a^2} \\
\Rightarrow \dfrac{1}{6} \times \dfrac{{2M}}{{\sqrt 3 \pi }} \times \dfrac{{4{R^2}}}{3} \\
\Rightarrow \dfrac{{4M{R^2}}}{{9\sqrt 3 \pi }} \\
$
So C is the correct option.
Additional Information: The term moment of inertia is also known as mass moment of inertia. It is defined as the ratio of net angular momentum of a system to its angular velocity around the principal axis. Moment of inertia plays a very important role in physics which means that in physics problems that involve the mass in rotation motion and that are calculated by angular momentum.
THERE ARE THREE TYPES OF INERTIA:
A.)INERTIA OF REST
B.)INERTIA OF MOTION
C.)INERTIA OF DIRECTION
If the moment of inertia is increased there will be a slowing down process of speed of rotation. We can also say that the moment of inertia of the body is directly proportional to the mass and it increases as the mass moves further from the axis of rotation.
Therefore option (C) is the right answer.
Note: Don’t get confused in saying that the moment of inertia and the inertia is the same in nature in physics. No it is not inertia means just the state of the body either it is in motion or rest whereas the moment of inertia is the measurement of resistances of the object against the rotation.
Step By Step Answer:
As we can see our cube diagonal is
$
\sqrt 3 a = 2R \\
\Rightarrow a = \dfrac{{2R}}{3} \\
$
As we say $ {M^ / } $is the mass of the cube so, material is same thus sphere density must equal to the cube density.
$
\dfrac{M}{{\dfrac{4}{3}\pi {R^3}}} = \dfrac{{{M^ / }}}{{{a^3}}} \\
\Rightarrow {M^ / } = \dfrac{{3M{a^3}}}{{4\pi {R^3}}}.......................................(a = 8) \\
\Rightarrow \dfrac{{3M}}{{4\pi {R^3}}} \times \dfrac{{8{R^3}}}{{3\sqrt 3 }} = \dfrac{{2M}}{{\sqrt 3 \pi }} \\
$
AS WE KNOW THAT MOMENT OF INERTIA IS:
$
I = \dfrac{1}{6}{M^ / }{a^2} \\
\Rightarrow \dfrac{1}{6} \times \dfrac{{2M}}{{\sqrt 3 \pi }} \times \dfrac{{4{R^2}}}{3} \\
\Rightarrow \dfrac{{4M{R^2}}}{{9\sqrt 3 \pi }} \\
$
So C is the correct option.
Additional Information: The term moment of inertia is also known as mass moment of inertia. It is defined as the ratio of net angular momentum of a system to its angular velocity around the principal axis. Moment of inertia plays a very important role in physics which means that in physics problems that involve the mass in rotation motion and that are calculated by angular momentum.
THERE ARE THREE TYPES OF INERTIA:
A.)INERTIA OF REST
B.)INERTIA OF MOTION
C.)INERTIA OF DIRECTION
If the moment of inertia is increased there will be a slowing down process of speed of rotation. We can also say that the moment of inertia of the body is directly proportional to the mass and it increases as the mass moves further from the axis of rotation.
Therefore option (C) is the right answer.
Note: Don’t get confused in saying that the moment of inertia and the inertia is the same in nature in physics. No it is not inertia means just the state of the body either it is in motion or rest whereas the moment of inertia is the measurement of resistances of the object against the rotation.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE