If a person with a spring balance and a body hanging from it goes up and up in an aeroplane, then the reading

Question

If a person with a spring balance and a body hanging from it goes up and up in an aeroplane, then the reading of the weight of the body as indicated by the spring balance will:

Accepted Answer

1. **Initial Ascent (Acceleration Phase):** When the aeroplane takes off and ascends, it accelerates vertically upwards with acceleration $a$. According to Newton's Second Law, the force (tension $T$ in the spring balance) is given by $T - mg = ma$, so $T = m(g + a)$. This apparent weight is greater than the actual weight ($mg$). Thus, the reading **increases** initially.
2. **High Altitude Phase (Variation of g):** As the aeroplane reaches higher altitudes ('goes up and up'), the acceleration due to gravity ($g$) decreases with height ($h$) according to the relation $g_h = g \frac{R^2}{(R+h)^2}$. As $g$ decreases, the weight ($mg'$) decreases.
3. **Cruising Phase:** Additionally, when the plane reaches a steady cruising altitude, the vertical acceleration $a$ becomes zero, returning the apparent weight to $mg'$ (which is already lower than ground $mg$ due to altitude). 
4. **Conclusion:** Consequently, the reading first increases due to the initial upward acceleration and subsequently decreases due to the decrease in gravity at high altitudes.
   (Reference: NCERT Class 11, Physics Part I, Chapter 5: Laws of Motion [Apparent Weight]; Chapter 8: Gravitation [Variation of g]).

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