Question Details

A body of mass 2 kg is hung on a spring balance mounted vertically in a lift. If the lift descends with an acceleration equal to the acceleration due to gravity ‘g’, the reading on the spring balance will be

Options

A

2 kg

B

(4 x g) kg

C

(2 x g) kg

D

Zero

Correct Answer :

Zero

Solution :

The correct answer is Zero.

Let us analyze the forces acting on the body of mass m = 2 kg inside the lift.
When the body is hung on a spring balance inside a lift, the spring balance measures the apparent weight (or the tension T in the spring) of the body.

When the lift is descending (moving downwards) with an acceleration a, the equation of motion for the body can be written by applying Newton's second law of motion:
mg - T = ma

Rearranging the equation to solve for the tension T (which represents the reading on the spring balance):
T = m(g - a)

According to the question, the lift descends with an acceleration equal to the acceleration due to gravity, which means:
a = g

Substituting a = g into the equation for tension:
T = m(g - g)
T = m(0)
T = 0

Since the tension in the spring balance is zero, the reading on the spring balance will be Zero. This state is commonly known as weightlessness or free fall.

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