1
AIEEE 2006
+4
-1
A thin circular ring of mass $$m$$ and radius $$R$$ is rotating about its axis with a constant angular velocity $$\omega$$. Two objects each of mass $$M$$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $$\omega ' =$$
A
$${{\omega \left( {m + 2M} \right)} \over m}$$
B
$${{\omega \left( {m - 2M} \right)} \over {\left( {m + 2M} \right)}}$$
C
$${{\omega m} \over {\left( {m + M} \right)}}$$
D
$${{\omega m} \over {\left( {m + 2M} \right)}}$$
2
AIEEE 2006
+4
-1
A force of $$- F\widehat k$$ acts on $$O,$$ the origin of the coordinate system. The torque about the point $$(1, -1)$$ is A
$$F\left( {\widehat i - \widehat j} \right)$$
B
$$- F\left( {\widehat i + \widehat j} \right)$$
C
$$F\left( {\widehat i + \widehat j} \right)$$
D
$$- F\left( {\widehat i - \widehat j} \right)$$
3
AIEEE 2005
+4
-1
An annular ring with inner and outer radii $${R_1}$$ and $${R_2}$$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $${{{F_1}} \over {{F_2}}}\,$$ is
A
$${\left( {{{{R_1}} \over {{R_2}}}} \right)^2}$$
B
$${{{{R_2}} \over {{R_1}}}}$$
C
$${{{{R_1}} \over {{R_2}}}}$$
D
$$1$$
4
AIEEE 2005
+4
-1
The moment of inertia of a uniform semicircular disc of mass $$M$$ and radius $$r$$ about a line perpendicular to the plane of the disc through the center is
A
$${2 \over 5}M{r^2}$$
B
$${1 \over 4}Mr$$
C
$${1 \over 2}M{r^2}$$
D
$$M{r^2}$$
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