- Two plates 1 and 2 move with velocities –v and 2v
respectively. If the sphere does not slide relative to
the plates, assuming the masses of each body as m.
The kinetic energy of the
system (plates + sphere)
is
x
mv
40(^2). The value of
x is
- A semi-circular track of radius R = 62.5 cm is cut in
a block. Mass of block, having track, is M = 1 kg and
rests over a smooth horizontal floor. A cylinder of
radius r = 10 cm and mass m = 0.5 kg is hanging by
a thread such that axes of cylinder and track are in
same level and surface of cylinder is in contact with
the track as shown in the figure. When the thread is
burnt, cylinder starts to move down the track.
Sufficient friction exists between
surface of cylinder and track,
so that cylinder does not slip.
Calculate velocity (in ms–1) of
axis of cylinder when it reaches
bottom of the track (g = 10 m s–2).
Comprehension TypeA uniform rod of length L lies on a smooth horizontal
table. The rod has a mass M. A particle of mass m
moving with speed v strikes the rod perpendicularly at
one of the ends of the rod and sticks to it after collision.
- Find the velocity of the centre of mass C of the
system constituting ‘the rod plus the particle’.
(a)2 Mv
Mm−(b)2 mv
Mm+(c)Mv
Mm+(d)mv
Mm+- Find the velocity of the rod with respect to C before
the collision
(a)
Mv
Mm+ (b)mv
Mm+ (c)2 Mv
Mm+ (d)2 mv
mM+
Matrix Match Type- From a uniform disc of mass M and radius R, a
concentric disc of radius R/2 is cut out.
For the remaining annular disc : I 1 is the moment of
inertia about axis ‘1’, I 2 about ‘2’, I 3 about ‘3’ and I 4
about ‘4’.
v m
m
m^2 v
2lmMRAxes ‘1’ and ‘2’ are
perpendicular to the disc
and ‘3’ and ‘4’ are in the
plane of the disc.
Axes ‘2’, ‘3’ and ‘4’
intersect at a common
point.
Match the following columns:
Column I Column II
(A) I 1 is equal to (P)21
32
MR^2
(B) I 2 is equal to (Q) I 1 /2(C) I 3 +I 4 is equal to (R)15
32
MR^2
(D) I 2 – I 3 is equal to (S) none of these
A B C D
(a) R P P Q
(b) P Q R S
(c) Q P R P
(d) R P R S- Match column I with column II.
A disc rolls on ground without slipping. Velocity of
centre of mass is v.
There is a point P on
circumference of disc at
angle q. Suppose vP is the
speed of this point. Then,
match the following
columns.
Column I Column II
(A)If q = 60° (P) vvP=^2
(B) If q = 90° (Q) vP = v
(C)If q = 120° (R) vP = 2 v
(D)If q = 180° (S) vvP= 3
A B C D
(a) P P S Q
(b) S R R S
(c) Q P S R
(d) R S Q P
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