1
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is Io as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is :

A
$${7 \over 8}$$ Io
B
$${15 \over 16}$$ Io
C
$${{3\,{{\rm I}_o}} \over 4}$$
D
$${{31\,{{\rm I}_o}} \over 32}$$
2
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct ?
A
Left arm is longer than the right arm
B
Both the arms are of same length
C
Left arm is shorter than the right arm
D
Every object that is weighed using this balance appears lighter than its actual weight.
3
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :

A
$${{2\,\,mg} \over {2\,m + M}}$$
B
$${{2\,\,Mg} \over {2\,m + M}}$$
C
$${{2\,\,mg} \over {2\,M + m}}$$
D
$${{2\,\,Mg} \over {2\,M + M}}$$
4
JEE Main 2017 (Offline)
+4
-1
The moment of inertia of a uniform cylinder of length $$l$$ and radius R about its perpendicular bisector is $$I$$. What is the ratio $${l \over R}$$ such that the moment of inertia is minimum?
A
$${3 \over {\sqrt 2 }}$$
B
$$\sqrt {{3 \over 2}}$$
C
$${{\sqrt 3 } \over 2}$$
D
1
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