Question

If the tension in the cable supporting a lift moving downwards is half the tension when it is moving upwards, the acceleration of the lift is

• A. \( \dfrac{g}{2} \)
• B. \( \dfrac{g}{3} \)
• C. \( \dfrac{g}{4} \)
• D. none of these

Hint:

For lifts: Upward acceleration → \( T = m(g + a) \)
Downward acceleration → \( T = m(g - a) \)

Answer 1

The Correct Option is B

Step 1: Writing expressions for tension.
Let the mass of the lift be \( m \) and acceleration be \( a \).
When the lift moves upwards with acceleration \( a \): \[ T_1 = m(g + a) \] When the lift moves downwards with acceleration \( a \): \[ T_2 = m(g - a) \]
Step 2: Applying the given condition.
It is given that the downward tension is half the upward tension: \[ T_2 = \frac{1}{2}T_1 \] Substituting values: \[ m(g - a) = \frac{1}{2}m(g + a) \]
Step 3: Solving for acceleration.
Canceling \( m \) and simplifying: \[ 2(g - a) = g + a \] \[ 2g - 2a = g + a \] \[ g = 3a \] \[ a = \frac{g}{3} \]
Step 4: Conclusion.
The acceleration of the lift is \( \dfrac{g}{3} \).