Game:

Counter-Strike: Source (2004)

Duration: 5:12

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Three particles \( A, B \) and \( C \), each of mass \( m \), are connected to each other by three massless rigid rods to form a rigid, equilateral triangular body of side \( l \). This body is placed on a horizontal frictionless table ( \( x-y \) plane) and is hinged to it at the point \( A \), so that it can move without friction about the vertical axis through \( A \) (see figure). The body is set into rotational motion on the table about \( A \) with a constant angular velocity \( \omega \).
(a) Find the magnitude of the horizontal force exerted by the hinge on the body.
(b) At time \( T \), when the side \( B C \) is parallel to the \( x \)-axis, a force \( F \) is applied on \( B \) along \( B C \) (as shown). Obtain the \( x \)-component and the \( y \)-component of the force exerted by the hinge on the body, immediately after time \( T \).
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