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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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The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is
$0_{0}$
. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is :
A
$0_{0}+2ML_{2} $
B
$0_{0}+4ML_{2} $
C
$0_{0}+2ML_{2}$
D
$0_{0}+ML_{2}$
Hard
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An automobile is started from rest with one of its doors initially at right angles. lf the hinges of the door are toward the front of the car, the door will shut as the automobile picks up speed. The acceleration a is constant and the centre of mass is at a distance d from the hinges. The time
$T$
needed for the doors to close is given by:
$[Given:∫_{0}sinθ dθ =N]$
(Consider the door as a square plate)
A
$T=(2a3d )N$
B
$T=(3ad )N$
C
$T=(a2d )N$
D
$T=(3a2d )N$
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 uniform sheet each of thickness 10 units is
cut into the shape as shown. Compute then x
and y-coordinates of the centre of mass of the
piece from point A.
A
17.5, 22.5
B
22.5, 17.5
C
10.5, 22.5
D
190/7, 125/7
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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In the system shown, a force of
$100$
N is applied at the end shown. What is the magnitude
$τ$
(in N-m) of the torque which was produced on the drum for starting motion? (Given that the coefficient of static friction is
$0.1$
)
A
$10$
B
$5$
C
$20$
D
$25$
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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