question_answer

A man of weight 80 kg is standing in an elevator which is moving with an acceleration of \[6\,m/{{s}^{2}}\]in upward direction. The apparent weight of the man will be \[(g=10\,\,m/{{s}^{2}})\]:

A)  148 N         

B)  128 N

C)  138 N         

D)  None of these

Correct Answer: B

Solution :

 Key Idea: When elevator is moving up, effective acceleration increases. When man is standing in an elevator going up, with an acceleration a the net force on the man is \[F=mg-R\] From Newtons second law of motion, the net force on him is F = - ma (downwards) \[\therefore \] \[-ma=mg-R\] \[\Rightarrow \] \[R=mg+ma\] Since, \[R=w\] \[w=m\,(g+a)\] Given,\[m=\frac{80}{10}=8\,kg,g=10\,m/{{s}^{2}},a=6\,m/{{s}^{2}}\] \[\therefore \] \[w=8\,(10+6)\,w=128\,N\] Note: When elevator is going up, weight of man is greater than the gravity force mg. That is, the man will feel his weight to be increased than in the normal state.