Question

A child stands on a weighing machine inside a lift. When the lift is going down with acceleration \(\mathrm{g} / 3\), the machine shows a reading 20 N . When the lift goes upwards with acceleration \(\mathrm{g} / 3\), the reading would be ( \(\mathrm{g}=\) gravitational acceleration)

• A. 40 N
• B. 30 N
• C. 20 N
• D. 50 N

Hint:

Apparent weight is m(g - a) when accelerating down and m(g + a) when accelerating up.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
The machine shows the normal force \(N\), which is the apparent weight.

Step 2: Going down
\(N=m\left(g-\dfrac{g}{3}\right)=\dfrac{2mg}{3}=20\text{ N}\Rightarrow mg=30\text{ N}\)

Step 3: Going up
\(N'=m\left(g+\dfrac{g}{3}\right)=\dfrac{4mg}{3}=\dfrac{4}{3}\times30=40\text{ N}\)

Final Answer:
The reading is 40 N. \[ \boxed{\text{(A) }40\ \text{N}} \]