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) \[{{\overrightarrow{F}}_{3}}=-{{\overrightarrow{F}}_{4}}\]

C) \[{{F}_{2}}>{{F}_{1}}\]                  

D) \[{{\overrightarrow{F}}_{2}}=-{{\overrightarrow{F}}_{4}}\]

Correct Answer: D

Solution :

FBD of various components of system is shown in figure. Since balloon is moving at constant speed, net force on balloon & student must be zero. On balloon some other force must be acting which is not mentioned. For equilibrium of student  \[{{\vec{F}}_{2}}+{{\vec{F}}_{4}}=0\Rightarrow {{\vec{F}}_{2}}=-{{\vec{F}}_{4}}.\] Relation between \[{{F}_{1}},{{F}_{2}}\]can't be known. \[{{\vec{F}}_{1}}\And {{\vec{F}}_{3}}\]are forming an action reaction pair.