A narrow but tall cabin is falling freely near the earth's surfac… - Vidyadip

MCQ

A narrow but tall cabin is falling freely near the earth's surface. Inside the cabin, two small stones $A$ and $B$ are released from rest (relative to the cabin). Initially $A$ is much above the centre of mass and $B$ much below the centre of mass of the cabin. A close observation of the motion of $A$ and $B$ will reveal that

A
both $A$ and $B$ continue to be exactly at rest relative to the cabin
✓
$A$ moves slowly upward and $B$ moves slowly downward relative to the cabin
C
both $A$ and $B$ fall to the bottom of the cabin with constant acceleration due to gravity
D
$A$ and $B$ move slightly towards each other vertically

✓

Answer

Correct option: B.

$A$ moves slowly upward and $B$ moves slowly downward relative to the cabin

b
(b)

Acceleration due to gravity decreases as we move up from the earth's surface.

Let $A$ and $B$ are stones and $C$ is centre of mass of cabin. 'Their positions given are as shown below.

Clearly, $a_B > a_C > a_A$.

Hence, $B$ is accelerated more than $C$ and $A$ is accelerated less than $C$.

So, with time $A$ move upwards and $B$ move downwards relative to the cabin. So, option $(b)$ is correct.

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