1
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0

A uniform rod $$\mathrm{AB}$$ of length $$1 \mathrm{~m}$$ and mass $$4 \mathrm{~kg}$$ is sliding along two mutually perpendicular frictionless walls OX and OY. The velocity of the two ends of the $$\operatorname{rod} \mathrm{A}$$ and $$\mathrm{B}$$ are $$3 \mathrm{~m} / \mathrm{s}$$ and $$4 \mathrm{~m} / \mathrm{s}$$ respectively, as shown in the figure. Then which of the following statement(s) is/are correct?

A
The velocity of the centre of mass of the rod is $$2.5 \mathrm{~m} / \mathrm{s}$$.
B
Rotational kinetic energy of the rod is $$\frac{25}{6}$$ joule.
C
The angular velocity of the rod is $$5 \mathrm{~rad} / \mathrm{s}$$ clockwise.
D
The angular velocity of the rod is $$5 \mathrm{~rad} / \mathrm{s}$$ anticlockwise.
2
WB JEE 2017
MCQ (More than One Correct Answer)
+2
-0
A small steel ball bounces on a steel plate held horizontally. On each bounce the speed of the ball arriving at the plate is reduced by a factor e (coefficient of restitution) in the rebound, so that Vupward = eVdownward. If the ball is initially dropped from a height of 0.4 m above the plate and if 10 seconds later the bouncing ceases, the value of e is
A
$$\sqrt {{2 \over 7}}$$
B
$${{3 \over 4}}$$
C
$${{{13} \over {18}}}$$
D
$${{{17} \over {18}}}$$
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