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11th Physics Weekly Test - 3 ( Motion of System of Particles and Rigid Bodies )

MABS Institution

11th Physics Weekly Test - 3 ( Motion of System of Particles and Rigid Bodies )-Aug 2020

Time : 1.00 Hours

Part - A

Multiple Choice Question - Answer All Question

Moment of inertia for bulk object

rm²
rw²
\(m_ir^{2}_{i}\)
\(\sum{m_ir^{2}_{i}}\)

Angular momentum is associated with

rotational motion
linear motion
both (a) and (b)
circular motion only

A couple is acting on a two particle system. The resultants motion will be:

purely rotational motion
purely linear motion
both (a) and (b)
neither (a) nor (b)

A sphere rolls down in an inclined plane without slipping. The percentage of translational energy in its total energy is

29.6%
33.4%
71.4%
50%

A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia,

A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle \(\theta\). The frictional force:

dissipates energy as heat
decreases the rotational motion
decreases the rotational and translational motion
converts translational energy to rotational energy

The changes produced by the deforming forces in a rigid body are

very large
infinity
negligibly small
small

A raw egg and hard boiled egg are made to spin on a table with the same angular speed about the sameaxis. The ratio of the time taken by the eggs to stop is

=1
<1
>1
none of these

A couple produces____ motion.

linear and rotational
purely rotational
purely linear
no

The rate of change of angular momentum is

Torque
angular velocity
centripetal force
centrifugal force

For square and rectangular objects center of mass lies at

the point where the diagonals meet
at the corners
on the center surface
any point

The direction of the angular velocity vector is along:

the tangent to the circular path
the inward radius
the outward radius
the axis of rotation

The ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. I_AB, I_BC and I_CA are the moments of inertia of the plate about AB, BC and CA respectively. Which one of the following relations is correct?

I_AB+I_BC=I_CA
I_CA is maximum
I_AB > I_BC
I_BC > I_AB

Rotational Kinetic energy of a body is

\(\frac { 1 }{ 2 } \)mr²
\(\frac { 1 }{ 2 } \)Iω²
\(\frac { 1 }{ 2 } \)Iv²
\(\frac { 1 }{ 2 } \)mω²

A mass M is moving with a constant velocity along a line parallel to the z-axis away from the origin. Its angular momentum with respect to the origin:

Zero
remains constant
goes on increasing
goes on decreasing

A round object of mass M and radius R rolls down without slipping along an inclined plane. The fractional force

dissipates kinetic energy as heat.
decreases the rotational motion.
decreases the rotational and transnational motion
converts transnational energy into rotational energy

Angular momentum is

\(\overrightarrow{p} \times \overrightarrow{r}\)
\(\overrightarrow{r}\times \overrightarrow{p}\)
\(\frac{\overrightarrow{r}}{\overrightarrow{p}}\)
\(\overrightarrow{r}.\overrightarrow{p}\)

An electron is revolving in an orbit of radius 2 A with a speed of 4 x 10⁵ m/s. The angular momentum of the electron is [M_e = 9 x 10^-31 kg]

2 x 10^-35 kg m² s^-1
72 x 10^-36 kg m² s^-1
7.2 x 10^-34 kg m² s^-1
0.72 x 10^-37 kg m² s^-1

A flywheel is attached to an engine to:

increase its speed
decrease its speed
help in overcoming the dead point
decrease its energy

In pure rolling, rotational velocity of points at its edges is equal to

Rω
velocity of centre of mass
translational velocity
all the above

Two discs of same material have the same mass. If their thicknesses are in the ratio 1:3, then their moments of inertia are in the ratio

3:1
1:3
1:9
\(1:\sqrt{3}\)

If a street light of mass M is suspended from the end of a uniform rod of length L in different possible patterns as shown in figure, then:

pattern A is more sturdy
pattern B is more sturdy
pattern C is more Sturdy
all will have same sturdiness

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D₁ has D₂ kg mass and 0.2 m radius and initial angular velocity of 50 cad s^-1, Disc D₂, has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s^-1The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s^-1) of the system is

60
100
120
40

A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes,

L
L/2
2L
L/\(\sqrt{2}\)

The moment of inertia of a body about a given axis is 1.2 kgm². Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration 25 radian/sec² must be applied about that axis lor a duration of

Moment of inertia of a solid cylinder having radius R₀ is:

\(MR_{0}^{2}\)
\(MR_{0}^{{2\over3}}\)
\(MR_{0}^{{2\over4}}\)
\(MR_{0}^{{2\over 2}}\)

If there is change of angular momentum from J to 4J in 4S, then the torque is

3/4 J
1J
5/4 J
4/3 J

From a disc of radius R a mass M, a circular hole of diameter R, whose rim passes through the center is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through it

15MR²/32
13MR²/32
llMR²/32
9MR²/32

Moment of inertia of a this uniform hollow cylinder about an axis passing perpendicular to the length and passing through the center is

MR²
M\(\left( \frac { { R }^{ 2 } }{ 2 } +\frac { { l }^{ 2 } }{ 12 } \right) \).
\(\frac { 1 }{ 2 } \)MR²
M\(\left( \frac { { R }^{ 2 } }{ 4 } +\frac { { l }^{ 2 } }{ 12 } \right) \).

The dimension of point mass is

positive
negative
zero
infinity

If the direction of the torque is inward the paper then the rotation is

clockwise
anticlockwise
straight line
random direction

If E is a rotational kinetic energy then angular momentum is

\(\sqrt { 2IE } \)
\(\frac { { E }^{ 2 } }{ 2I } \).
\(\frac { 2I }{ { E }^{ 2 } } \).
\(\frac { E }{ { I }^{ 2 }{ \omega }^{ 2 } } \).

Time taken by the rolling object in inclined plane to reach its bottom is

\(\sqrt { \frac { 1+\frac { { k }^{ 2 } }{ { R }^{ 2 } } }{ gsin^{ 2 }\theta } } \).
\(\sqrt { \frac { 2gh }{ 1+\frac { { k }^{ 2 } }{ { R }^{ 2 } } } } \).
\(\sqrt { \frac { 2h\left( 1+\frac { { k }^{ 2 } }{ { R }^{ 2 } } \right) }{ gsin^{ 2 }\theta } } \).
\(\sqrt { \frac { 2h\left( 1+\frac { { k }^{ 2 } }{ { R }^{ 2 } } \right) }{ gsin^{ 2 }\theta } } \)

The torque in rotational motion is analogous to __________ in translational motion

linear momentum
mass
couple
force

A circular disk of moment of inertia l₁is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed \(\omega_i\) Another disk of moment of inertia I_b is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed \(\omega_t\)The energy lost by the initially rotating disc to friction is

\({1\over2}{I^2_b\over(I_t+I_b)}\omega^2_i\)
\({1\over2}{I^2_t\over(I_t+I_b)}\omega^2_i\)
\({I_b-I_t\over(I_t+I_b)}\omega^2_i\)
\({1\over2}{I_bI_t\over(I_t+I_b)}\omega^2_i\)

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