question_answer

With what minimum acceleration can a fireman slide down a rope whose breaking strength is two third of his weight?

A)  \[\frac{g}{m}\]                                

B)  \[\frac{2}{3}g\]

C)  \[\frac{3}{2}g\]                               

D)  \[\frac{g}{2}\]

Correct Answer: A

Solution :

                 Let a be the resultant acceleration with which the fireman slides down, then                                 \[mg-T=ma\] Given,   \[{{T}_{m}}=\frac{2}{3}mg\],      \[a={{a}_{m}}\] \[\therefore \]  \[mg-\frac{2}{3}mg=m{{a}_{m}}\] \[\Rightarrow \]               \[{{a}_{m}}=g-\frac{2}{3}g=\frac{g}{3}\]