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Standard XII

Physics

Applying NLM along 3 Axis

A balloon of ...

Question

A balloon of mass M is descending at a constant acceleration $α$ . When a mass m is released from the balloon, it starts rising with the same acceleration $α$ . Assuming that its volume does not change, what is the value of m?

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Solution

The correct option is B

Suppose F = upthrust due to buoyancy
Then while descending, we find Mg - F = M $α$ ..............................(i)

When ascending, we have F - (M - m)g = (M - m) $α$ ....................(ii)

Solving Eqs. (i) and (ii), we get $m = [\frac{2 α}{α + g}] M$

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A balloon of mass M is descending at a constant acceleration α. When a mass m is released from the balloon, it starts rising with the same acceleration α. Assuming that its volume does not change, what is the value of m?

The correct option is B Suppose F = upthrust due to buoyancy Then while descending, we find Mg - F = Mα..............................(i) When ascending, we have F - (M - m)g = (M - m) α ....................(ii) Solving Eqs. (i) and (ii), we get m=[2αα+g]M

A balloon of mass M is descending at a constant acceleration $α$ . When a mass m is released from the balloon, it starts rising with the same acceleration $α$ . Assuming that its volume does not change, what is the value of m?

The correct option is B

Suppose F = upthrust due to buoyancy
Then while descending, we find Mg - F = M $α$ ..............................(i)

When ascending, we have F - (M - m)g = (M - m) $α$ ....................(ii)

Solving Eqs. (i) and (ii), we get $m = [\frac{2 α}{α + g}] M$