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Question


One end of the light inelastic string is tied to a helium filled balloon and its other end is tied to the bottom of a water-filled container at point O. The container lies on a fixed horizontal surface and is pulled horizontally towards the right with a constant horizontal acceleration of magnitude a.
Assuming no relative motion of balloon and water with respect to the container, the string will be inclined with the vertical line passing through O by an angle:

(g is acceleration due to gravity)

71923.jpg

A
θ=tan1ag and string will be on right of vertical line passing through O.
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B
θ=tan1ga and string will be on right of vertical line passing through O.
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C
θ=tan1ag and string will be on left of vertical line passing through O.
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D
θ=tan1ga and string will be on left of vertical line passing through O.
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Solution

The correct option is C θ=tan1ag and string will be on left of vertical line passing through O.
Let the density of gas and water by ρg and ρw.
The volume enclosed by balloon is V.
Then the FBD of balloon is as shown.
Hence, in
equilibrium: tanθ=FxFy=ag
278250_71923_ans.png

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