question_answer

A student in a hot air balloon ascends vertically at constant speed. Consider the following four forces that arise in this situation

\[{{F}_{1}}\]: The weight of the hot air balloon

\[{{F}_{2}}\]: The weight of the student

\[{{F}_{3}}\]: The force of the student pulling on the earth

\[{{F}_{4}}\]: The force of the hot air balloon pulling on the student

Which of the following relationships concerning the forces or their magnitudes is true?

A)  \[{{F}_{4}}>{{F}_{2}}\]  

B)  \[{{F}_{3}}=-{{F}_{4}}\]

C)  \[{{F}_{2}}>{{F}_{1}}\]  

D)  \[{{F}_{2}}=-{{F}_{4}}\]

Correct Answer: D

Solution :

 Free body diagram of various components of the system is as shown in figure. Since, balloon is moving at constant speed, net force on balloon and student must be zero. On balloon some other force must be acting which is not mentioned. For equilibrium of the student. \[{{F}_{2}}+{{F}_{4}}=0\] \[\Rightarrow \]          \[{{F}_{2}}=-{{F}_{4}}\] Relation between, \[{{F}_{1}}\] and \[{{F}_{2}}\] cannot be known.