1
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motoin of angular frequency $$\omega .$$ The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
A
at the mean position of the platform
B
for an amplitude of $${g \over {{\omega ^2}}}$$
C
For an amplitude of $${{{g^2}} \over {{\omega ^2}}}$$
D
at the height position of the platform
2
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
A particle of mass $$100g$$ is thrown vertically upwards with a speed of $$5$$ $$m/s$$. The work done by the force of gravity during the time the particle goes up is
A
$$-0.5J$$
B
$$-1.25J$$
C
$$1.25J$$
D
$$0.5J$$
3
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
The potential energy of a $$1$$ $$kg$$ particle free to move along the $$x$$-axis is given by $$V\left( x \right) = \left( {{{{x^4}} \over 4} - {{{x^2}} \over 2}} \right)J$$.

The total mechanical energy of the particle is $$2J.$$ Then, the maximum speed (in $$m/s$$) is

A
$${3 \over {\sqrt 2 }}$$
B
$${\sqrt 2 }$$
C
$${1 \over {\sqrt 2 }}$$
D
$$2$$
4
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
A bomb of mass $$16kg$$ at rest explodes into two pieces of masses $$4$$ $$kg$$ and $$12$$ $$kg.$$ The velocity of the $$12$$ $$kg$$ mass is $$4\,\,m{s^{ - 1}}.$$ The kinetic energy of the other mass is
A
$$144$$ $$J$$
B
$$288$$ $$J$$
C
$$192$$ $$J$$
D
$$96$$ $$J$$
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