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Physics
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Systems of Particles and Rotational Motion
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Hard Questions
Systems Of Particles And Rotational Motion
Physics
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BITSAT
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Four thin metal rods, each of mass
$M$
and length
$L$
, are welded to form a square. The moment of inertia of the composite structure about a line which bisects any two opposite rods is:
A
$6ML_{2} $
B
$3ML_{2} $
C
$2ML_{2} $
D
$32ML_{2} $
Hard
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Three identical spheres each of mass m and radius R are placed touching each other so that their centres A, B and C lie on a straight line. The position of their centre of mass from the centre of A is
A
$32R $
B
2R
C
$35R $
D
$34R $
Hard
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A uniform circular disc of mass
$1.5kg$
and radius
$0.5m$
is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude
$0.5N$
are applied simultaneously along the three sides of an equilateral triangle
$XYZ$
with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular speed of the disc in
$rads_{−1}$
is:
A
$2$
B
$4$
C
$5$
D
$7$
Hard
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Three identical thin rods each of mass
$m$
and length
$L$
are joined together to form an equilateral triangular frame. The moment of inertia of frame about an axis perpendicular to the plane of frame and passing through a corner is:
A
$32mL_{2} $
B
$23mL_{2} $
C
$34mL_{2} $
D
$43mL_{2} $
Hard
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A horizontal circular platform of radius
$0.5m$
and mass
$0.45kg$
is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass
$0.05kg$
are attached to the platform at a distance
$0.25m$
from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the ball horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the ball have horizontal speed of
$9ms$
$_{−1}$
with respect to the ground. The rotational speed of the platform in
$rads$
$_{−1}$
after the balls leave the platform is :
Hard
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Two particles A and B are revolving with constant angular velocity on two concentric circles of radius
$1m$
and
$2m$
respectively as shown in figure. The positions of the particles at
$t=0$
are shown in figure. If
$m_{A}=2kg$
,
$m_{B}=1kg$
and
$P_{A}$
and
$P_{B}$
are linear momentum of the particles then what is the maximum value of
$∣P_{A}+P_{B}∣$
in
$kgm/s$
in subsequent motion of the two particles.
A
$1$
B
$7$
C
$8$
D
$5$
Hard
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Two small balls
$A$
and
$B$
are made of same material,
$A$
is solid but
$B$
is hollow. These are connected by an ideal spring and this system is kept over a smooth plank such that center of mass of two balls coincide with mid point of the plank. Initially the spring is compressed by a certain amount and the plank is in horizontal position. Now we release the system then,
A
Plank will rotate clock wise
B
Plank will rotate anti clock wise
C
Plank will not rotate
D
It will depend upon string constant.
Hard
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A thin uniform metallic triangular sheet of mass M has sides
$AB=BC=L$
. Its moment of inertia about the axis AC lying in the plane of the sheet is:
A
$12ML_{2} $
B
$6ML_{2} $
C
$3ML_{2} $
D
$32ML_{2} $
Hard
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A car (open at the top) of mass 9.75 kg is coasting along a level track at 1.36 m/s, when it begins to rain hard. The raindrops fall vertically with respect to the ground. When it has collected 0.5 kg of rain, the speed of the car is
A
0.68 m/s
B
1.29 m/s
C
2.48 m/s
D
9.8 m/s
Hard
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A uniform rod AB of mass m and length
$ℓ$
is in equilibrium with the help of two identical inextensible strings as shown in the figure. Choose the correct option (s)
A
After cutting the string (2) motion of centre of mass of the rod is circular
B
After cutting the string (2) motion of centre of mass of the rod is not circular
C
Just after cutting the string (2) the acceleration of point A along the string (1) is zero.
D
Just after cutting the string (2) the acceleration of point A perpendicular to the string (1) is not zero.
Hard
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