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KVPY 2020-21 SA Exam Previous Papers
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© examsnet.com
Question : 24
Total: 80
Figure below shows a shampoo bottle in a perfect cylindrical shape.
In a simple experiment, the stability of the bottle filled with different amount of shampoo volume is observed. The bottle is tilted from one side and then released. Let the angle θ depicts the critical angular displacement resulting, in the bottle losing its stability and tipping over. Choose the graph correctly depicting the fraction f of shampoo filled (f = 1 corresponds to completely filled) vs the tipping angle θ
Validate
Solution:
A the point of vertical angular displacement, the gravitational force would pass via point of contact. This would lead to zero torque about point of contact.
h : height of shampoo
h
0
: height of bottle
R : Radius of bottle
tan
θ
=
R
(
h
2
)
=
2
R
h
⇒
tan
θ
=
2
R
h
0
f
⇒
θ
=
tan
−
1
(
2
R
h
0
f
)
(
∵
h
h
0
=
f
)
© examsnet.com
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