1
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
A spherical ball of mass $$20$$ $$kg$$ is stationary at the top of a hill of height $$100$$ $$m$$. It rolls down a smooth surface to the ground, then climbs up another hill of height $$30$$ $$m$$ and finally rolls down to a horizontal base at a height of $$20$$ $$m$$ above the ground. The velocity attained by the ball is
A
$$20$$ $$m/s$$
B
$$40$$ $$m/s$$
C
$$10\sqrt {30} \,\,\,m/s$$
D
$$10\,\,m/s$$
2
AIEEE 2005
MCQ (Single Correct Answer)
+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
$$M{r^2}$$
3
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
A body $$A$$ of mass $$M$$ while falling vertically downloads under gravity breaks into two-parts; a body $$B$$ of mass $${1 \over 3}$$ $$M$$ and a body $$C$$ of mass $${2 \over 3}$$ $$M.$$ The center of mass of bodies $$B$$ and $$C$$ taken together shifts compared to that of bodies $$B$$ and $$C$$ taken together shifts compared to that of body $$A$$ towards
A
does not shift
B
depends on height of breaking
C
body $$B$$
D
body $$C$$
4
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
A particle of mass $$10$$ $$g$$ is kept on the surface of a uniform sphere of mass $$100$$ $$kg$$ and radius $$10$$ $$cm.$$ Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $$G$$ $$ = 6.67 \times {10^{ - 11}}\,\,N{m^2}/k{g^2}$$)
A
$$3.33 \times {10^{ - 10}}\,J$$
B
$$13.34 \times {10^{ - 10}}\,J$$
C
$$6.67 \times {10^{ - 10}}\,J$$
D
$$6.67 \times {10^{ - 9}}\,J$$
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