An elevator weighing 6000 kg is pulled upward by a cable with an acceleration of 5 ms⁻² . Taking g to be 10 ms⁻² , then the tension in the cable is

The correct option is 90000 N.

To find the tension in the cable pulling the elevator upward, we can analyze the forces acting on the elevator.
Let us identify the given values from the problem statement:
• Mass of the elevator, m = 6000 kg
• Upward acceleration of the elevator, a = 5 ms^-2
• Acceleration due to gravity, g = 10 ms^-2

When the elevator is accelerated upward, two main vertical forces act on it:
1. The tension in the cable (T) acting vertically upward.
2. The gravitational force or weight of the elevator (W = mg) acting vertically downward.

According to Newton's second law of motion, the net force acting on the elevator is equal to the product of its mass and its acceleration:
$$F_{\text{net}}=m\cdot a$$

Since the acceleration is directed upward, the tension T must be greater than the downward gravitational force mg. Therefore, the net upward force is:
$$F_{\text{net}}=T-mg$$

Equating the two expressions for the net force, we get:
$$T-mg=ma$$

Rearranging the equation to solve for the tension (T):
$$T=mg+ma$$
$$T=m(g+a)$$

Now, substitute the given numerical values into the formula:
$$T=6000\hspace{0.17em}\text{kg}\cdot (10\hspace{0.17em}{\text{ms}}^{-2}+5\hspace{0.17em}{\text{ms}}^{-2})$$
$$T=6000\cdot 15$$
$$T=90000\hspace{0.17em}\text{N}$$

Thus, the tension in the cable is 90000 N.