1
AIEEE 2011
+4
-1
A pulley of radius $$2$$ $$m$$ is rotated about its axis by a force $$F = \left( {20t - 5{t^2}} \right)$$ newton (where $$t$$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $$10kg$$-$${m^2}$$ the number of rotation made by the pulley before its direction of motion is reversed, is:
A
more than $$3$$ but less than $$6$$
B
more than $$6$$ but less than $$9$$
C
more than $$9$$
D
less than $$3$$
2
AIEEE 2010
+4
-1
A small particle of mass $$m$$ is projected at an angle $$\theta$$ with the $$x$$-axis with an initial velocity $${v_0}$$ in the $$x$$-$$y$$ plane as shown in the figure. At a time $$t < {{{v_0}\sin \theta } \over g},$$ the angular momentum of the particle is ................,

where $$\widehat i,\widehat j$$ and $$\widehat k$$ are unit vectors along $$x,y$$ and $$z$$-axis respectively.
A
$$- mg\,{v_0}{t^2}\cos \theta \widehat j$$
B
$$mg\,{v_0}t\cos \theta \widehat k$$
C
$$- {1 \over 2}mg\,{v_0}{t^2}\cos \,\theta \widehat k$$
D
$${1 \over 2}mg\,{v_0}{t^2}\cos \theta \widehat i$$
3
AIEEE 2009
+4
-1
A thin uniform rod of length $$l$$ and mass $$m$$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $$\omega$$. Its center of mass rises to a maximum height of:
A
$${1 \over 6}\,\,{{l\omega } \over g}$$
B
$${1 \over 2}\,\,{{{l^2}{\omega ^2}} \over g}$$
C
$${1 \over 6}\,\,{{{l^2}{\omega ^2}} \over g}$$
D
$${1 \over 3}\,\,{{{l^2}{\omega ^2}} \over g}$$
4
AIEEE 2008
+4
-1
Consider a uniform square plate of side $$' a '$$ and mass $$'m'$$. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
A
$${5 \over 6}m{a^2}$$
B
$${1 \over 12}m{a^2}$$
C
$${7 \over 12}m{a^2}$$
D
$${2 \over 3}m{a^2}$$
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