A block of mass m rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is $$0.25.$$ The string can withstand a maximum force of $$20$$ N. The maximum value of the mass (m) for which the string will not break and the block will be in static equilibrium is ____________ kg.
Take $$\cos \theta = 0.8$$ and $$\sin \theta = 0.6$$. Acceleration due to gravity g $$=$$ $$10$$ m/s²

A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in the barrel. Projections A and B on the bullet engage in each of the slots.
Helical slots are such that one turn of helix is completed over a distance of 0.5m. If velocity of bullet when it exits the barrel is 20m/s, its spinning speed (in rad/s) is ________

The initial velocity of an object is $$40$$ $$m/s.$$ The acceleration a of the object is given by the following expression: a$$=-0.1v$$
Where v is the instantaneous velocity of the object. The velocity of the object after $$3$$ seconds will be _______

For the truss shown in the figure, the magnitude of the force (in kN) in the member SR is