Question

With what minimum acceleration can an athletic climb a rope whose breaking strength is $\frac{1}{3}$rd of his weight?

• A. $6.53 \,m/s^2$
• B. $7 \,m/s^2$
• C. $8 \,m/s^2$
• D. $7.23 \,m/s^2$

Answer 1

Answer: (A)

$T = m ( g + a )$
$ T = mg \left(1+\frac{ a }{ g }\right)$
$\frac{ Mg }{3}= Mg \left(1+\frac{ a }{ g }\right) $
$\Rightarrow \frac{1}{3}=1+\frac{ a }{ g }$
$\Rightarrow \frac{ a }{ g }=1-\frac{1}{3}$
$\frac{ a }{ g }=\frac{2}{3} $
$ \Rightarrow a =6.53 m / s ^{2}$