A uniform thin stick of length ℓ and mass m is held horizontally with its end B hinged at a point B on the edge of a table. Point A is suddenly released. The acceleration of the centre of mass of the

Question

A uniform thin stick of length ℓ and mass m is held horizontally with its end B hinged at a point B on the edge of a table. Point A is suddenly released. The acceleration of the centre of mass of the stick at the time of release, is :-

TestHub · Accepted Answer

Torque acting about the point B is ( mg ) 2 ℓ ​ I α = ( mg ) 2 ℓ ​ ⇒ α = 2 I mg ℓ ​ a = α ( 2 ℓ ​ ) = 4 I mg ℓ 2 ​ I = 3 m ℓ 2 ​ ⇒ a = 4 ( 3 m ℓ 2 ​ ) mg ℓ 2 ​ = 4 3 ​ g τ = mg ( 2 ℓ ​ ) = I α I = ( 3 m ℓ 2 ​ ) ⇒ mg ( 2 ℓ ​ ) = ( 3 m ℓ 2 ​ ) α ⇒ α = ( 2 ℓ 3 g ​ ) The acceleration of the center of mass is: = α ( 2 ℓ ​ ) = ( 2 ℓ 3 g ​ ) ( 2 ℓ ​ ) = 4 3 ​ g

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