Lower surface of a plank is rough and lying at rest on a rough horizontal surface. Upper surface of the plank is smooth and has a smooth hemisphere placed over it through a light string as shown in the figure. After the string is burnt, trajectory of centre of mass of the sphere is:

a circle

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an ellipse

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a stright line

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a parabola

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Solution

The correct option is C a stright line
Here, after burning the string, there is no external force acting on the hemisphere except gravity. So, the centre of mass will move straight downward.

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