Q.
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 water with the string inclined at an angle θ to the horizontal. Assuming that the density of ball is half the density of water, if, then m=310kg find the tension in the string (in N). (Take g = 10 m/s2)
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answer is 100.0.
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Detailed Solution
As the container is accelerating the liquid surface will be inclined with horizontal such thattanθ=ag=g/3g=13Hence sinθ=110 and cosθ=310In this case the bouncy force on the ball will be natural to water surface. The magnitude of bouncy forceB=Vdisρwgeff⇒ B=mρρwg2+a2=2mg2+g29which gives B=2103mgThe force acting on the ball are shown in F.B.D. (w.r.t. container)As the ball is in equilibrium with respect to container, thenB=T+mgcosθ+masinθ2103mg=T+mg⋅310+mg3⋅110⇒ T=103mg=103×310×10=100N
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