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JEE Advanced 2021 Paper 1
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© examsnet.com
Question : 11
Total: 57
A horizontal force
F
is applied at the center of mass of a cylindrical object of mass
m
and radius
R
, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is
µ
. The center of mass of the object has an acceleration
a
. The acceleration due to gravity is
g
. Given that the object rolls without slipping, which of the following statement(s) is(are) correct?
For the same
F
, the value of a does not depend on whether the cylinder is solid or hollow
For a solid cylinder, the maximum possible value of a is
2
µ
g
The magnitude of the frictional force on the object due to the ground is always
µ
m
g
For a thin-walled hollow cylinder,
a
=
F
2
m
Validate
Solution:
For solid cylinder,
F
×
R
=
3
2
m
R
3
×
(
a
R
)
⇒
a
=
2
F
m
For hollow cylinder,
F
×
R
=
(
2
m
R
2
)
×
a
R
⇒
a
=
F
2
m
For solid cylinder
f
=
F
−
m
×
2
F
3
m
=
F
3
≤
µ
m
g
⇒
F
≤
3
µ
m
g
∴
a
max
=
2
µ
g
© examsnet.com
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