Question

A lift of mass 1000 kg which is moving with acceleration of $1 m/s^2$ in upward direction, then the tension developed in string which is connected to lift is :-

• A. 9800 N
• B. 10,800 N
• C. 11,000 N
• D. 10,000 N

Answer 1

The Correct Option is B

To find the tension developed in the string connected to the lift moving upward with acceleration, we need to apply Newton's second law. The tension in the string (T) is given by considering the forces acting on the lift.

Step 1: Identify the forces acting on the lift

• Gravitational force (weight) acting downward: ${F_{\text{gravity}} = mg}$
• Tension in the string acting upward: T

Where:

• m = 1000\, \text{kg} (mass of the lift)
• g = 9.8\, \text{m/s}^2 (acceleration due to gravity)
• a = 1\, \text{m/s}^2 (acceleration of the lift)

Step 2: Apply Newton's second law

The net force acting on the lift is given by the equation:

F_{\text{net}} = ma

Since the lift is accelerating upwards, the equation relating the forces is:

T - mg = ma

Step 3: Solve for the tension (T)

Rearranging the equation to solve for T gives:

T = ma + mg

Substitute the given values:

T = (1000\, \text{kg}) \cdot (1\, \text{m/s}^2) + (1000\, \text{kg}) \cdot (9.8\, \text{m/s}^2)

T = 1000 + 9800

T = 10800\, \text{N}

Conclusion

The tension developed in the string connected to the lift is 10,800\, \text{N}.