1
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
The machine as shown has 2 rods of length1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

A
Constant speed
B
decreasing speed
C
increasing speed
D
speed which is $${3 \over 4}$$th of that of the roller when the weight is 0.4 m above the ground
2
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
A circular hole of radius $${R \over 4}$$ is made in a thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is :

A
$${{219\,M{R^2}} \over {256}}$$
B
$${{237\,M{R^2}} \over {512}}$$
C
$${{19\,M{R^2}} \over {512}}$$
D
$${{197\,M{R^2}} \over {256}}$$
3
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
$${{31\,{{\rm I}_o}} \over 32}$$
4
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.
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