1
AIEEE 2006
+4
-1
Consider a two particle system with particles having masses $${m_1}$$ and $${m_2}$$. If the first particle is pushed towards the center of mass through a distance $$d,$$ by what distance should the second particle is moved, so as to keep the center of mass at the same position?
A
$${{{m_2}} \over {{m_1}}}\,\,d$$
B
$${{{m_1}} \over {{m_1} + {m_2}}}d$$
C
$${{{m_1}} \over {{m_2}}}d$$
D
$$d$$
2
AIEEE 2005
+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 $$C$$
3
AIEEE 2005
+4
-1
The block of mass $$M$$ moving on the frictionless horizontal surface collides with the spring of spring constant $$k$$ and compresses it by length $$L.$$ The maximum momentum of the block after collision is
A
$${{k{L^2}} \over {2M}}$$
B
$$\sqrt {Mk} \,\,L$$
C
$${{M{L^2}} \over k}$$
D
Zero
4
AIEEE 2005
+4
-1
A mass $$'m'$$ moves with a velocity $$'v'$$ and collides inelastically with another identical mass. After collision the $${1^{st}}$$ mass moves with velocity $${v \over {\sqrt 3 }}$$ in a direction perpendicular to the initial direction of motion. Find the speed of the $${2^{nd}}$$ mass after collision.
A
$${\sqrt 3 v}$$
B
$$v$$
C
$${v \over {\sqrt 3 }}$$
D
$${2 \over {\sqrt 3 }}v$$
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