Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force $$\overrightarrow P $$ of magnitude 100 N is applied at point A of the frame.


Suppose the force is $$\overrightarrow P $$ resolved parallel to the arms AB and AC of the frame.

The magnitude of the resolved component along the arm AC is xN.

The value of x, to the nearest integer, is ___________.

[Given : sin(35$$^\circ$$) = 0.573, cos(35$$^\circ$$) = 0.819

sin(110$$^\circ$$) = 0.939, cos(110$$^\circ$$) = $$-$$ 0.342 J

A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is _______ $$\times$$ 10^$$-$$1 kg m².

A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1 kg moving in a straight line with velocity 80 m/s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad/s) of the rod immediately after the collision will be _________.

A force $$\overrightarrow F = \left( {\widehat i + 2\widehat j + 3\widehat k} \right)$$ N acts at a point
$$\left( {4\widehat i + 3\widehat j - \widehat k} \right)$$ m. Then the magnitude of torque
about the point $$\left( {\widehat i + 2\widehat j + \widehat k} \right)$$ m will be $$\sqrt x $$ N m.
The value of x is _______.