Question:
With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is $\frac23$ of the weight?
With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is $\frac23$ of the weight?
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With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is $\frac23$ of the weight?
Updated On: Apr 15, 2026
- $\frac{2}{3}g$
- g
- $\frac{1}{3}g$
- Zero
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The Correct Option is C
Solution and Explanation
Step 1: Apparent Weight
When sliding down with acceleration $a$, the tension in the rope (apparent weight) is $T = m(g-a)$.
Step 2: Condition
The tension must not exceed the breaking strength: $T \leq \frac{2}{3}mg$.
Step 3: Calculation
$m(g-a) = \frac{2}{3}mg$. $g-a = \frac{2}{3}g \Rightarrow a = g - \frac{2}{3}g = \frac{1}{3}g$.
Final Answer: (C)
When sliding down with acceleration $a$, the tension in the rope (apparent weight) is $T = m(g-a)$.
Step 2: Condition
The tension must not exceed the breaking strength: $T \leq \frac{2}{3}mg$.
Step 3: Calculation
$m(g-a) = \frac{2}{3}mg$. $g-a = \frac{2}{3}g \Rightarrow a = g - \frac{2}{3}g = \frac{1}{3}g$.
Final Answer: (C)
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