1
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
$${1 \over 3}\,\,{{{l^2}{\omega ^2}} \over g}$$
2
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
$${2 \over 3}m{a^2}$$
3
AIEEE 2008
+4
-1
A thin rod of length $$'L'$$ is lying along the $$x$$-axis with its ends at $$x=0$$ and $$x=L$$. Its linear density (mass/length) varies with $$x$$ as $$k{\left( {{x \over L}} \right)^n},$$ where $$n$$ can be zero or any positive number. If the position $${X_{CM}}$$ of the center of mass of the rod is plotted against $$'n',$$ which of the following graphs best approximates the dependence of $${X_{CM}}$$ on $$n$$?
A B C D 4
AIEEE 2007
+4
-1
A circular disc of radius $$R$$ is removed from a bigger circular disc of radius $$2R$$ such that the circumferences of the discs coincide. The center of mass of the new disc is $$\alpha R$$ form the center of the bigger disc. The value of $$\alpha$$ is
A
$$1/4$$
B
$$1/3$$
C
$$1/2$$
D
$$1/6$$
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