wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A solid sphere moves at a terminal velocity of 20 ms1 in air at a place where g=9.8 ms2. The sphere is taken in a gravity free hall having air at the same pressure and pushed downwards at a speed of 20 ms1. Then, identify the correct statement(s):
[Assume density of air to be very low.]

A
Intial acceleration of sphere will be 9.8 ms2 downwards.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Initial acceleration of sphere will be 9.8 ms2 upwards.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
The magnitude of acceleration of the sphere will decrease as time passes.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
Sphere will eventually stop.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D Sphere will eventually stop.
Since there is no gravity, there will be no initial acceleration in downward direction. Hence the option (a) is incorrect.
20 m/s is the terminal velocity. At this velocity, the viscous force is equal to the weight of the sphere (assuming the buoyant force to be negligible because air has a very low density).
i.e Fv=mg at v=20 m/s

When sphere is thrown downwards at a speed of 20 m/s, once again, viscous force Fv=mg will act vertically upwards.
W=mg=0 [since gravity free space]
a=Fvm=mgm=g
The sphere gets an initial acceleration a=9.8 m/s2 in upward direction.
Hence option (b) is correct.

Fv acting in opposite direction of velocity will cause retardation in the sphere. Hence, its velocity will decrease continously.
Fvv
Fv as v
Hence, magnitude of acceleration (retardation) also reduces as time passes.
Option (c) is correct

Since the viscous force (Fv) continously opposes the motion of the sphere, it will eventually stop i.e at some instant v=0 will be achieved.
Hence, the option (d) is also correct.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon