Q198 / 200 · Manipal (MET) 2010 · Physics

With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is $\frac{2}{3}$ of the weight?

  • A
    $\frac{2}{3} g$
  • B
    $g$
  • Correct answer
    C
    $\frac{1}{3} g$
  • D
    zero

Solution

If man slides down with some acceleration, then its apparent weight decreases. For critical condition rope can bear only $2 / 3$ of his weight. If $a$ is the minimum acceleration, then tension in the rope $=m(g-a)$ = breaking strength $\Rightarrow \quad m(g-a)=\frac{2}{3} m g$ $\Rightarrow \quad a=g-\frac{2 g}{3}=\frac{g}{3}$

Hence, the correct answer is option: 'C'.

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