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 introduced by the spring balance will.
\[A.\] goes on increasing
$B.$ goes on decreasing
$C.$ first increase and then decrease.
$D.$ remains the same.

Answer 1

- Hint: Since aeroplane is accelerating it will create a pseudo force on the person which will act in downward direction, also acceleration due to gravity decreases as we go up from the earth surface. Use these two pieces of information to get the answer.

Complete step-by-step solution -
Let the acceleration of aeroplane is $a$.
According to Newton's 3rd law of motion “ If a body is accelerating with acceleration $a$ then force acting on it would be given by $F = ma$ . “ This force would create a pseudo-force on the body acting in downward direction which will be equal to $ma$ .
Also gravitational force acting on a body = mg, where g is acceleration due to gravity.
So total force acting on the body would be,
$F = $ $ma + mg$ ,
Now as we know that acceleration due to gravity at a height h above earth surface is given by,
$g' = g(1 - \dfrac{{2h}}{R})$
From the above formula it is clear that acceleration due to gravity decreases as we go above the earth surface.
So from this we can deduce that first there will be an increase in reading of spring balance due to the pseudo force but after some time there will be decrease in the reading due decrease in acceleration due to gravity.
So option C is the correct answer.

Note: This question is similar to the case as if we pull a spring which has a mass hanging from it suddenly then it expands because there is an additional force acting on it downward, but here one more case happens when the body goes above earth then value of g decreases, that’s why reading first increases then decreases.