A uniform metallic spherical shell is suspended from ceiling- It has two holes A and B at top and bottom respectively- Which of the following is true -A- If B is closed and sand is poured from A- centre of mass first rises and then fallsB- If shell is completely filled with sand and B is opened then centre of mass falls initially-C- none of theseD- If shell is slightly filled with sand and B is opened- then centre of mass falls-

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Question

A uniform metallic spherical shell is suspended from ceiling. It has two holes $A$ and $B$ at top and bottom respectively. Which of the following is true ?

B

is closed and sand is poured from

A

, centre of mass first rises and then falls

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If shell is completely filled with sand and

B

is opened then centre of mass falls initially.

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If shell is slightly filled with sand and

B

is opened, then centre of mass falls.

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none of these

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Solution

The correct option is B If shell is completely filled with sand and $B$ is opened then centre of mass falls initially.
When sand starts falling from $A$ , CM falls down from each centre of hollow sphere then it again rises and finally when sand is fully filled, centre of mass is again at centre of sphere.
Now when $B$ is opened, CM again starts falling down.

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A uniform metallic spherical shell is suspended from ceiling. It has two holes A and B at top and bottom respectively. Which of the following is true ?

A uniform metallic spherical shell is suspended from ceiling. It has two holes $A$ and $B$ at top and bottom respectively. Which of the following is true ?