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)

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 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)

Infinity Learn · Accepted Answer

As the container is accelerating the liquid surface will be inclined with horizontal such thattan⁡θ$$=ag=g/3g=13Hence$$ $$sin$$⁡θ$$=110$$ and $$cos$$⁡θ$$=310In$$ this case the bouncy force on the ball will be natural to water surface. The magnitude of bouncy $$forceB=Vdis$$ρwgeff⇒ $$B=m$$ρρ$$wg2+a2=2mg2+g29which$$ 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, $$thenB=T+mgcos$$⁡θ$$+masin$$⁡θ$$2103mg=T+mg$$⋅$$310+mg3$$⋅$$110$$⇒ $$T=103mg=103$$×$$310$$×$$10=100N$$

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!