Question

A person of mass \( 60 \) kg is inside a lift of mass \( 940 \) kg. The lift starts moving upwards with an acceleration of \( 1.0 \) m/s\( ^2 \). If \( g = 10 \) m/s\( ^2 \), the tension in the supporting cable is:

• A. \( 8600 \) N
• B. \( 9680 \) N
• C. \( 11000 \) N
• D. \( 1200 \) N

Hint:

In an accelerating lift, the apparent weight is given by \( T = mg + ma \).

Answer 1

The Correct Option is C

Step 1: {Determine total mass}
\[ m_{{total}} = 60 + 940 = 1000 { kg} \] Step 2: {Use Newton’s Second Law}
\[ T - mg = ma \] Substituting values: \[ T - (1000 \times 10) = 1000 \times 1 \] \[ T = 10000 + 1000 = 11000 { N} \] Thus, the correct answer is (C) 11000 N.

Answer 2

To determine the tension in the supporting cable, we need to consider both the gravitational and the additional force due to the acceleration of the lift.

Given:

• Mass of person \(m_1 = 60\) kg
• Mass of lift \(m_2 = 940\) kg
• Total mass \(m = m_1 + m_2 = 60 + 940 = 1000\) kg
• Acceleration \(a = 1.0\) m/s²
• Acceleration due to gravity \(g = 10\) m/s²

The net acceleration (upward direction) is \(a\), so using Newton's second law:

\[ T - mg = ma \]

Solve for \(T\):

\[ T = m(g + a) \]

Substitute the known values:

\[ T = 1000 \times (10 + 1) = 1000 \times 11 = 11000 \text{ N} \]

Therefore, the tension in the cable is 11000 N.