(i) Liquid of density `rho` flows at speed `upsilon` along a flexible pipe bent into a semicircle of radius R. The cross sectional area of the pipe is A and its cross sectional radius is small compared to R. Three strings `S_(1), S_(2) and S_(3)` keep the pipe in place. `S_(3)` ties the two ends of the pipe and the other two string have their ends secured at A and B. Strings `S_(1) and S_(2)` are perpendicular to the string `S_(3)`. The entire system is in horizontal plane. Find the tension in the three strings

(ii) A car of mass `M` is moving with a velocity `V_(0)` on a smooth horizontal surface. Bullets, each of mass m, are fired horizontally perpendicular to the velocity of the car with a speed `u` relative to the car. After firing n bullets it was found that the car was travelling with velocity `V_(0)` in a direction opposite to its original direction of motion. Assume that mu `lt lt MV_(0)` and also that nm `lt lt M`. Find n in terms of other given parameters.

Answer

(i) `T_(s1)=T_(s2)=T_(s3)=rhoAv^(2)`
(ii) `(pi MV_(0))/(m u)`