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Question

A container partially filled with water is moved horizontally with acceleration a=g3 . A small wooden ball of mass m is tied to the bottom of the container using a string. The ball remains inside the water with the string inclined at an angle θ  to the horizontal. Assuming that the density of wood is half the density of water, and if the tension in the string is xmg, find  x.  
(Answer upto two digit after the decimal point)


Solution

As the container is accelerating the liquid surface will be inclined such that 

tanα=ag=13

Hence sinα=110 and cosα=310

In this case the buoyant force on the ball will be normal to water surface. The magnitude of buoyant force 

B=Vdisρwgeff 
B=mρρwg2+a2=2mg2+g29

which gives B=2103mg
The force acting on the ball are shown in FBD (w.r.t container), then
B=T+mg cosα+ma sinα
2103mg=T+mg.310+mg3.110

T=103mg

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