A weight of 500N is supported by two metallic ropes as shown in the figure. The values of tensions T₁ and T₂ are respectively.

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 ________

Which of the following statement are TRUE, when the cavitation parameter $$\sigma = 0?$$
(i) The local pressure is reduced to vapor pressure.
(ii) Cavitation starts
(iii) Boiling of liquid starts
(iv) Cavitations stops

A Prandtl tube (Pitot-static tube with $$C=1$$) is used to measure the velocity of water. The differential manometer reading is $$10$$ mm of liquid column with a relative density of $$10.$$ Assuming $$g = 9.8\,\,m/{s^2},$$ the velocity of water (in $$m/s$$) is ___________