Question

The mass of lift is 2000 kg. When the tension in the supporting cable is 28000 N, then its acceleration is:

• A. $14m{s}^{-2}$
• B. $30m{s}^{-2}$
• C. $4m{s}^{-2}$
• D. $40m{s}^{-2}$

Answer 1

The correct option is C $4m{s}^{-2}$

$\text{Step 1: Draw the free body diagram [Ref. Fig.]}$

Let $a$ be the acceleration of the lift in the upward direction.

$\text{Step 2: Applying Newton's second law}$

Applying Newton's second law on the lift:

$\Sigma F=ma$

$\Rightarrow T-mg=ma$ $....\left(1\right)$

$\text{Step 3: Substitute the values}$

From equation $\left(1\right)$

$\Rightarrow a=\frac{T-mg}{m}=\frac{28000N-2000kg\times 10m/s^2}{2000kg}=4m/s^2$

Hence, Option(C) is correct.