1
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
A wheel is rotating freely with an angular speed $$\omega$$ on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :
A
0
B
$${5 \over 6}$$
C
$${1 \over 4}$$
D
$${3 \over 4}$$
2
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
Consider two uniform discs of the same thickness and different radii R1 = R and
R2 = $$\alpha$$R made of the same material. If the ratio of their moments of inertia I1 and I2 , respectively, about their axes is I1 : I2 = 1 : 16 then the value of $$\alpha$$ is :
A
$$\sqrt 2$$
B
2
C
$$2\sqrt 2$$
D
4
3
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is :
A
$${1 \over 2}$$
B
$${1 \over 4}$$
C
$${1 \over 8}$$
D
$${2 \over 3}$$
4
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
A uniform rod of length ‘$$l$$’ is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed $$\omega$$ the rod makes an angle $$\theta$$ with it (see figure). To find $$\theta$$ equate the rate of change of angular momentum (direction going into the paper) $${{m{l^2}} \over {12}}{\omega ^2}\sin \theta \cos \theta$$ about the centre of mass (CM) to the torque provided by the horizontal and vertical forces FH and FV about the CM. The value of $$\theta$$ is then such that :
A
$$\cos \theta = {{2g} \over {3l{\omega ^2}}}$$
B
$$\cos \theta = {{3g} \over {2l{\omega ^2}}}$$
C
$$\cos \theta = {g \over {2l{\omega ^2}}}$$
D
$$\cos \theta = {g \over {l{\omega ^2}}}$$
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