A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released in starts performing simple harmonic motion at angular frequency omega. If the radius of the bottle is 2.5 cm then omega is close

A cylindrical plastic bottle of negligible mass is filled with 310 ml

1.	A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released in starts performing simple harmonic motion at angular frequency omega. If the radius of the bottle is 2.5 cm then omega is close
Answer» `2.50 rad"/"s` `3.75 rad"/"s` `5.00 rad"/"s` `1.25 rad"/"s` Solution :ACCORDING to law of floatation, (Weight of FLOATING object)= (Weight of LIQUID displaced by floating object) `therefore mg = m_(0)g` `therefore m= m_(0) implies V. p_(0)= Alp_(0)` `implies l= (m)/(A p_(0))= (m)/(pi R^(2) p_(0))` `therefore l= (310g)/((3.14)(2.5 cm)^(2)(1-(g)/(cm^3))) approx 16 cm approx 0.16 m` Now angular frequency, `omega = sqrt((g)/(l)) = sqrt((9.8)/(0.16))= sqrt(61.25)= 7.826 (rad)/(s)` The nearest value in GIVEN options for above answer is `5 rad"/"s`. `therefore omega approx 5.0 (rad)/(s)`.