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QJEEM21Ph948b: JEE Main 2021 Physics - Class 11 JEEM21Ph948b Solution: Four equal masses, m each are placed at the comers of a square…

Four equal masses, m each are placed at the comers of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be :

JEE Main 2021 (Online) 16th March Morning Shift Physics - Center of Mass and Collision Question 58 English

Multiple Choice Options

  • A 3\sqrt 3 ml2
  • B 2 ml2
  • C ml2
  • D 3 ml2

Step-by-Step Verified Solution

JEE Main 2021 (Online) 16th March Morning Shift Physics - Center of Mass and Collision Question 58 English Explanation
AC=l2+l2AC = \sqrt {{l^2} + {l^2}}

AC=l2AC = l\sqrt 2

d=l22d = {{l\sqrt 2 } \over 2}

⇒d=12\Rightarrow d = {1 \over {\sqrt 2 }}

Moment of inertia about the axis passing through A :

I=m(O)2+m(d)2+m(d)2+M(AC)2I = m{(O)^2} + m{(d)^2} + m{(d)^2} + M{(AC)^2}

⇒I=O+m(l2)2+m(l2)2+m(l2)2\Rightarrow I = O + m{\left( {{l \over {\sqrt 2 }}} \right)^2} + m{\left( {{l \over {\sqrt 2 }}} \right)^2} + m{\left( {l\sqrt 2 } \right)^2}

⇒I=ml22+ml22+2ml2\Rightarrow I = {{m{l^2}} \over 2} + {{m{l^2}} \over 2} + 2m{l^2}

⇒I=3ml2\Rightarrow I = 3m{l^2}

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