question_answer

A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car.  The car is moving with constant acceleration a directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration a vertically. The tension in the string is equal to               

A) \[m\sqrt{{{g}^{2}}+{{a}^{2}}}\]  

B) \[m\sqrt{{{g}^{2}}+{{a}^{2}}}-ma\]

C) \[m\sqrt{{{g}^{2}}+{{a}^{2}}}+ma\]           

D) \[m\left( g+a \right)\]

Correct Answer: C

Solution :

[c] (Force diagram in the frame of the car) Applying Newton?s law along string \[\Rightarrow T-m\sqrt{{{g}^{2}}+{{a}^{2}}}=ma\] \[\text{or }T=m\sqrt{{{g}^{2}}+{{a}^{2}}}+ma\]