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Rotational Motion

148 Questions Start Allen Test
All Exams Allen Objective Errorless
Q1 Allen KINEMATICS OF ROTATIONAL MOTION MCQ
Which of the following pairs do not match :-
A.
rotational power–Joule/sec
B.
torque-Newton meter
C.
angular displacement-radian
D.
angular acceleration - radian/sec
Q2 Allen KINEMATICS OF ROTATIONAL MOTION MCQ
All the particles of a rigid rotating body move in a circular path when the axis of rotation:-
A.
passes through any point in the body
B.
is situated outside the body
C.
situated any where
D.
passes through the centre of mass
Q3 Allen KINEMATICS OF ROTATIONAL MOTION MCQ
On account of the earth rotating about its axis :-
A.
the linear velocity of objects at equator is greater than at other places.
B.
the angular velocity of objects at equator is more than that of objects at poles.
C.
the linear velocity of objects at all places at the earth is equal, but angular velocity is different.
D.
at all places the angular velocity and linear velocity are uniform.
Q4 Allen KINEMATICS OF ROTATIONAL MOTION MCQ
The quantity not involved directly in rotational motion of the body is
A.
moment of inertia
B.
torque
C.
angular velocity
D.
mass PRM004
Q5 Allen MOMENT OF INERTIA MCQ
The moment of inertia of a body about a given axis of rotation depends upon :-
A.
the distribution of mass
B.
distance of particle of body from the axis of rotation
C.
shape of the body
D.
all of the above
Q6 Allen MOMENT OF INERTIA MCQ
A fly wheel is so constructed that almost whole of its mass is concentrated at its rim, because:-
A.
it increases the moment of inertia of the fly-wheel
B.
it decreases the moment of inertia of the fly-wheel
C.
it increases the speed of the fly-wheel
D.
it increases the power of the fly-wheel
Q7 Allen MOMENT OF INERTIA MCQ
The moment of inertia of a solid cylinder about its own axis is the same as its moment of inertia about an axis passing through its centre of gravity and perpendicular to its length. The relation between its length L and radius R is
A.
$\mathrm { L } = \sqrt { 2 } \mathrm { R }$
B.
$\mathsf { L } = \sqrt { 3 } \mathsf { R }$
C.
$\mathrm { L } = 3 \mathrm { R }$
D.
$\mathrm { L } = \mathrm { R }$
Q8 Allen MOMENT OF INERTIA MCQ
Four similar point masses (each of mass m) are placed on the circumference of a disc of mass M and radius R. The M.I. of the system about the normal axis through the centre O will be:-
A.
$$\mathrm{MR} ^ {2} + 4 \mathrm{mR} ^ {2}<br /> $$
B.
$\frac { 1 } { 2 } \mathrm { M R } ^ { 2 } + 4 \mathrm { m R } ^ { 2 }$
C.
$\mathbf { M } \mathbf { R } ^ { 2 } + \frac { 8 } { 5 } \mathbf { m } \mathbf { R } ^ { 2 }$
D.
none of these
Q9 Allen MOMENT OF INERTIA MCQ
By the theorem of perpendicular axes, if a body be in X-Z-plane then :-
A.
$\mathrm { { I } _ { x } - \mathrm { { I } _ { y } = \mathrm { { I } _ { z } } } }$
B.
$\mathrm { { I } _ { x } + \mathrm { { I } _ { z } = \mathrm { { I } _ { y } } } }$
C.
$\mathrm { { I _ { x } + I _ { y } = I _ { z } } }$
D.
$\mathrm { I } _ { \mathrm { y } } + \mathrm { I } _ { \mathrm { z } } = \mathrm { I } _ { \mathrm { x } }$
Q10 Allen MOMENT OF INERTIA MCQ
The theorem of perpendicular axes is not applicable for determination of moment of inertia along the diameter, for which of the following body :-
A.
sphere
B.
disc
C.
ring
D.
blade
Q11 Allen MOMENT OF INERTIA MCQ
The axes $X$ and $Z$ in the plane of a disc are mutually perpendicular and the $Y$-axis is perpendicular to the plane of the disc. If the moment of inertia of the body about the $X$ and $Y$ axes is respectively $30,\text{kg m}^2$ and $40,\text{kg m}^2$, then the moment of inertia about the $Z$-axis, in $\text{kg m}^2$, will be:
A.
$70$
B.
$50$
C.
$10$
D.
$0$
Q12 Allen MOMENT OF INERTIA MCQ
A solid sphere and a hollow sphere of the same mass have the same M.I. about their respective diameters. The ratio of their radii will be :-
A.
1 : 2
B.
${ \sqrt { 3 } } : { \sqrt { 5 } }$
C.
${ \sqrt { 5 } } : { \sqrt { 3 } }$
D.
$5 : 4$
Q13 Allen MOMENT OF INERTIA MCQ
The moment of inertia of a square lamina about the perpendicular axis through its centre of mass is $20,\text{kg}\cdot\text{m}^2$. Then, its moment of inertia about an axis touching its side and lying in the plane of the lamina will be:
A.
$10,\text{kg}\cdot\text{m}^2$
B.
$30,\text{kg}\cdot\text{m}^2$
C.
$40,\text{kg}\cdot\text{m}^2$
D.
$25,\text{kg}\cdot\text{m}^2$
Q14 Allen MOMENT OF INERTIA MCQ
The M.I. of a thin rod of length ℓ about the perpendicular axis through its centre is I. The M.I. of the square structure made by four such rods about a perpendicular axis to the plane and through the centre will be :-
A.
4I
B.
8I
C.
12I
D.
16I
Q15 Allen MOMENT OF INERTIA MCQ
The curve for the moment of inertia of a sphere of constant mass M versus distance of axis from its centre ?
A.
B.
C.
D.
Q16 Allen MOMENT OF INERTIA MCQ
The moment of inertia of a ring of mass $M$ and radius $R$ about the $PQ$ axis will be:
A.
$MR^2$
B.
$\dfrac{MR^2}{2}$
C.
$\dfrac{3}{2}MR^2$
D.
$2MR^2$
Q17 Allen MOMENT OF INERTIA MCQ
Four point masses (each of mass m) are arranged it the X-Y plane the moment of inertia of this array of masses about Y-axis is
A.
$\mathtt { m a } ^ { 2 }$
B.
$2 \mathrm { m a } ^ { 2 }$
C.
$4 \mathrm { { m a } } ^ { 2 }$
D.
6ma2
Q18 Allen MOMENT OF INERTIA MCQ
Which of the following has the highest moment of inertia when each of them has the same mass and the same radius ?
A.
a hollow sphere about one of its diameters
B.
a solid sphere about one of its diameters
C.
a disc about its central axis perpendicular to the plane of the disc
D.
a ring about its central axis perpendicular to the plane of the ring.
Q19 Allen MOMENT OF INERTIA MCQ
If the radius of gyration of a solid disc of mass $10,\text{kg}$ about an axis is $0.40,\text{m}$, then the moment of inertia of the disc about that axis is:
A.
$1.6,\text{kg},\text{m}^2$
B.
$3.2,\text{kg},\text{m}^2$
C.
$6.4,\text{kg},\text{m}^2$
D.
$9.5,\text{kg},\text{m}^2$
Q20 Allen MOMENT OF INERTIA MCQ
If ${ \mathrm { I } } _ { 1 } ,$ I and $\mathrm { I } _ { 3 }$ are moments of inertia of solid sphere, hollow sphere and a ring of same mass and radius about geometrical axis, which of the following statement holds good ?
A.
$\mathrm { I } _ { 1 } > \mathrm { I } _ { 2 } > \mathrm { I } _ { 3 }$
B.
$\mathrm { I } _ { 3 } > \mathrm { I } _ { 2 } > \mathrm { I } _ { 1 }$
C.
$\mathrm { I } _ { 2 } > \mathrm { I } _ { 1 } > \mathrm { I } _ { 3 }$
D.
$\mathrm { I } _ { 2 } > \mathrm { I } _ { 3 } > \mathrm { I } _ { 1 }$
Q21 Allen MOMENT OF INERTIA MCQ
Three thin uniform rods each of mass M and length L are placed along the three axis of a cartesian coordinate system with one end of each rod at the origin. The M. I. of the system about z-axis is
A.
$\frac { \mathrm { { M L } ^ { 2 } } } { 3 }$
B.
$\frac { 2 \mathrm { M L } ^ { 2 } } { 3 }$
C.
$\frac { \mathrm { { M L } ^ { 2 } } } { 6 }$
D.
$\mathrm { M L } ^ { 2 }$
Q22 Allen MOMENT OF INERTIA MCQ
Four particles each of mass m are placed at the corners of a square of side length . The radius of gyration of the system about an axis perpendicular to the square and passing through centre is :–
A.
$\frac { \ell } { \sqrt { 2 } }$
B.
$\frac { \ell } { 2 }$
C.
$\ell$
D.
$\ell \sqrt { 2 }$
Q23 Allen MOMENT OF INERTIA MCQ
The moment of inertia of a rod of mass M and length L about an axis passing through one edge and perpendicular to its length will be :–
A.
$\frac { \mathrm { { M L } ^ { 2 } } } { 1 2 }$
B.
$\frac { \mathrm { { M L } ^ { 2 } } } { 6 }$
C.
$\frac { \mathrm { { M L } ^ { 2 } } } { 3 }$
D.
$\mathrm { { M L } } ^ { 2 }$
Q24 Allen MOMENT OF INERTIA MCQ
A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with:
A.
aluminium at interior and iron surrounded to it.
B.
iron at interior and aluminium surrounded to it.
C.
using iron and aluminium layers in alternate order.
D.
sheet of iron is used at both external surface and aluminium sheet as internal layer.
Q25 Allen MOMENT OF INERTIA MCQ
The moment of inertia in rotational motion is equivalent to :–
A.
angular velocity of linear motion
B.
mass of linear motion
C.
frequency of linear motion
D.
current