Question and Answers Forum

AllQuestion and Answers: Page 28

Question Number 223724 Answers: 2 Comments: 0

A rubber ball of mass m radius R and densityρ is released from a depth h under a fluid of density σ(σ>ρ) i) How high will the ball bounce on the the fluid ?Ignore any obstacles ii)time taken by the ball to reach the surface iii)time in air

$$\: \\ $$$$\mathrm{A}\:\mathrm{rubber}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{m}\: \\ $$$$\mathrm{radius}\:\mathrm{R}\:\mathrm{and}\:\mathrm{density}\rho\:\mathrm{is}\:\mathrm{released}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{depth}\:\mathrm{h}\:\mathrm{under}\:\mathrm{a}\:\mathrm{fluid}\:\mathrm{of}\:\mathrm{density}\:\sigma\left(\sigma>\rho\right) \\ $$$$\left.\mathrm{i}\right) \\ $$$$\:\mathrm{How}\:\mathrm{high}\:\mathrm{will}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{bounce}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{the}\:\mathrm{fluid}\:?\mathrm{Ignore}\:\mathrm{any} \\ $$$$\mathrm{obstacles} \\ $$$$\left.\mathrm{ii}\right)\mathrm{time}\:\mathrm{taken}\:\mathrm{by}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{the}\: \\ $$$$\mathrm{surface} \\ $$$$\left.\mathrm{iii}\right)\mathrm{time}\:\mathrm{in}\:\mathrm{air} \\ $$

Question Number 223720 Answers: 1 Comments: 1

One end of a string is attached to a solid wall and the other end is hanging from a smooth pulley 2 m away fromthe wall. A point mass M of mass 2 kg is attached to the string 1 m away from the wall and an object m of mass 0.5 kg is attached to the hanging end of the string. The object is fixed in such a way that the part of the string inside the wall and pully is horizontal and the rest is vertical. If mass m is released, with what speed will mass M hit the wall?

$$ \\ $$$$\mathrm{One}\:\mathrm{end}\:\mathrm{of}\:\mathrm{a}\:\mathrm{string}\:\mathrm{is} \\ $$$$\mathrm{attached}\:\mathrm{to}\:\mathrm{a}\:\mathrm{solid}\:\mathrm{wall}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{end}\:\mathrm{is}\:\mathrm{hanging}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{smooth}\:\mathrm{pulley}\:\mathrm{2}\:\mathrm{m}\:\mathrm{away}\: \\ $$$$\mathrm{fromthe}\:\mathrm{wall}.\:\mathrm{A}\:\mathrm{point}\:\mathrm{mass}\: \\ $$$$\mathrm{M}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{attached}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{string}\:\mathrm{1}\:\mathrm{m}\:\mathrm{away}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{wall}\:\mathrm{and}\:\mathrm{an}\:\mathrm{object}\:\mathrm{m}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\mathrm{0}.\mathrm{5}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{attached}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{hanging}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{string}.\: \\ $$$$\mathrm{The}\:\mathrm{object}\:\mathrm{is}\:\mathrm{fixed}\:\mathrm{in}\:\mathrm{such}\:\mathrm{a} \\ $$$$\mathrm{way}\:\mathrm{that}\:\mathrm{the}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{string}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{and} \\ $$$$\mathrm{pully}\:\mathrm{is}\:\mathrm{horizontal}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{rest}\:\mathrm{is}\:\mathrm{vertical}.\:\mathrm{If}\:\mathrm{mass}\:\mathrm{m}\:\mathrm{is} \\ $$$$\mathrm{released},\:\mathrm{with}\:\mathrm{what}\:\mathrm{speed}\:\mathrm{will} \\ $$$$\mathrm{mass}\:\mathrm{M}\:\mathrm{hit}\:\mathrm{the}\:\mathrm{wall}? \\ $$

Question Number 223712 Answers: 3 Comments: 1