Question

A spherical ball falls through a viscous medium
with terminal velocity v. If this ball is replaced by
another ball of the same mass but half the radius,
then the terminal velocity will be (neglect effect
of buoyancy) :​

Answer 1

Answer:

Correct option is B)

In case of spherical ball

m=

3

4

πr

3

ρ

keeping m constant, if r is halved, ρ will increased by a factor of 8;

If buoyancy is neglected,

V

T

∝r

2

ρ; otherwise V

T

∝r

2

(ρ−ρ

o

)

⇒

V

T

V

T

′

=

r

2

ρ

r

′

2

ρ

′

⇒

V

T

V

T

′

=

r

2

ρ

(

2

r

)

2

8ρ

⇒

V

T

V

T

′

=

r

2

ρ

2r

2

ρ

⇒

V

T

V

T

′

=2

⇒V

T

′

=2V

T

⇒

V

T

′

=2v