Question

A fireman wants to slide down a rope. The rope can bear a tension of $\frac{3}{4}$ of the weight of the man. With what minimum acceleration should the fireman slide down?

• A. $\frac{g}{2}$
• B. $\frac{g}{3}$
• C. $\frac{g}{4}$
• D. $\frac{g}{6}$

Answer 1

The correct option is C

$\frac{g}{4}$

Step 1: Given data

The rope can bear a tension of $\frac{3}{4}$ of the weight of the man.

Step 2: Formula used

Force can be given as,

$$\begin{gathered} F=ma \\ Where,Fisforce,mismassandaisacceleration. \end{gathered}$$

Step 3: Calculating the minimum acceleration

Newton's second law states that the force required to accelerate a body is equal to the product of its mass and acceleration. The acceleration will be smaller for a large mass. As a result, more force is required to accelerate the body.

The force is imparted through the rope as the firefighter slides down it. Tension is the force exerted on the rope.

The minimum tension at the rope when the fireman slide down is given as,

$mg-\frac{3}{4}mg$

This force equating with the minimum tension at the rope, we get

$$\begin{gathered} ma=mg-\frac{3}{4}mg \\ a=g-\frac{3}{4}g \\ a=g\left(1-\frac{3}{4}\right) \\ a=\frac{g}{4} \end{gathered}$$

The fireman should slide down with a minimum acceleration of $\frac{1}{4}$ of the acceleration due to gravity.

Hence, option C is the correct answer.