Question

Tension of a rope when a man of mass \( m \) climbs up or down with an acceleration \( a<g \)?

• A. \( T = mg \)
• B. \( T = m(g - a) \)
• C. \( T = m(g + a) \)
• D. \( T = \frac{mg}{a} \)

Hint:

When climbing down, the tension in the rope is reduced by the downward acceleration. Similarly, climbing up would increase the tension due to the upward acceleration.

Answer 1

The Correct Option is B

The tension in the rope depends on the direction of motion and the acceleration. When the man is climbing up or down, the force required to lift or lower the body is affected by the acceleration.

1. Step 1: Analyze the forces. - When climbing up, the force exerted on the rope must overcome gravity, and the net force is also affected by the upward acceleration. Therefore, the tension in the rope is increased by the acceleration. - When climbing down, the force exerted on the rope is reduced by the downward acceleration. The tension in the rope is therefore less than the force due to gravity. The tension when the man climbs down is given by: \[ T = m(g - a) \] This shows that the tension is reduced by the acceleration \( a \). Thus, the correct answer is \( T = m(g - a) \).