A non-homogeneous thin rod A B of mass 2 M & length L is kept as shown in figure with the help of two rigid hinge supports at its end. The mass per unit length of rod is λ = k x 2 where K is a positiv

Question

A non-homogeneous thin rod A B of mass 2 M & length L is kept as shown in figure with the help of two rigid hinge supports at its end. The mass per unit length of rod is λ = k x 2 where K is a positive constant and x is distance from end A . Friction is absent everywhere then choose the CORRECT options.

TestHub · Accepted Answer

x c m ​ = 2 + 2 2 + 1 ​ L = 4 3 L ​ R B ​ ⋅ L = ( 2 M g ) ⋅ 4 3 L ​ ⟹ R B ​ = 2 3Mg ​ R A ​ = 2 M g − R B ​ = 2 Mg ​ λ = k x 2 , I A ​ = 5 3 ​ M L 2 τ = I A ​ α ( 2 M g ) ( 4 3 L ​ ) = ( 5 6 ​ M L 2 ) α ⟹ α = 4 L 5 g ​ h = x c m ​ = 4 3 L ​ . ( 2 M g ) ( 4 3 L ​ ) = 2 1 ​ I A ​ ω 2 2 3 ​ M gL = 2 1 ​ ( 5 6 ​ M L 2 ) ω 2 ⟹ ω = 2 L 5 g ​ ​

Physics - Rotation Question with Solution | TestHub

Options:(select one or more)

Doubts & Discussion

JEE Advanced 2026