A) decreases by \[mgh\]
B) increases by \[mgh\]
C) increases by \[mg(1-h)\]
D) increases by \[mgl\]
Correct Answer: B
Solution :
[a] The height climbed by the man is\[l\]. So the work done by the person is\[mgl\]. So the correct option for Q. No. 52 is [b]. But since the person falls into the balloon and comes down by a height \[h\] along with the balloon, the person loses a potential energy of\[mgh\]. Thus his final potential energy is equal to the work done by him minus the potential energy lost by him. His initial potential energy is zero. So his overall potential energy increases by\[mg(l-h)\]. So the correct option for Q. No. 50 is [a]. When the person falls downwards by a height\[h\], he loses a potential energy of\[mgh\]. This must also be equal to the gain in potential energy of the balloon. So, the correct option for Q. No. 51 is [b]. It can also justified by considering that the balloon has been pulled downwards by a sudden force mg for a height h (as in case of springs). The work done on the balloon in pulling it downwards gets stored in the balloon in the form of its elastic potential energy of the balloon. Hence its potential energy increases.
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