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Rotational Motion

148 Questions Start Allen Test
All Exams Allen Objective Errorless
Q26 Allen 2. MOMENT OF INERTIA MCQ
Two rods each of mass m and length $\ell$ are joined at the centre to form a cross. The moment of inertia of this cross about an axis passing through the common centre of the rods and perpendicular to the plane formed by them, is :–
A.
$\frac { { \mathrm { m } } { \mathrm { \ell } } ^ { 2 } } { 1 2 }$
B.
$\frac { \mathrm { m } \ell ^ { 2 } } { 6 }$
C.
$\frac { \mathrm { m } \ell ^ { 2 } } { 3 }$
D.
$\frac { \mathrm { m } \ell ^ { 2 } } { 2 }$
Q27 Allen 2. MOMENT OF INERTIA MCQ
The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is :–
A.
$2 : 1$
B.
${ \sqrt { 5 } } : { \sqrt { 6 } }$
C.
$2 : 3$
D.
$1 { : } { \sqrt { 2 } }$
Q28 Allen 2. MOMENT OF INERTIA MCQ
Three particles, each of mass $m$, are situated at the vertices of an equilateral triangle $ABC$ of side $\ell$ (as shown in the figure). The moment of inertia of the system about a line $AX$ perpendicular to $AB$ and lying in the plane of $ABC$, will be:
A.
$2m\ell^2$
B.
$\dfrac{5}{4}m\ell^2$
C.
$\dfrac{3}{2}m\ell^2$
D.
$\dfrac{3}{4}m\ell^2$
Q29 Allen 2. MOMENT OF INERTIA MCQ
A solid cylinder of mass 20kg has length 1 m and radius 0.2 m. Then its moment of inertia (in $\mathrm { k g - m } ^ { 2 } )$ about its geometrical axis is :–
A.
$0 . 8 \mathrm { k g } – \mathrm { m } ^ { 2 }$
B.
$0 . 4 \mathrm { k g } – \mathrm { m } ^ { 2 }$
C.
$0 . 2 \mathrm { k g } – \mathrm { m } ^ { 2 }$
D.
$20.2 kg-m^2$
Q30 Allen 2. MOMENT OF INERTIA MCQ
The moment of inertia of a circular ring (radius R, mass M) about an axis which passes through tangentially and perpendicular to its plane will be:–
A.
$\frac { \mathrm { M R } ^ { 2 } } { 2 }$
B.
$\mathrm { M R } ^ { 2 }$
C.
$\frac { 3 } { 2 } { \mathrm { M R } } ^ { 2 }$
D.
$2 \mathsf { M R } ^ { 2 }$
Q31 Allen 2. MOMENT OF INERTIA MCQ
What is the moment of inertia of ring about its diameter ?
A.
MR2
B.
$\frac { \mathrm { M R } ^ { 2 } } { 2 }$
C.
$\frac { 3 } { 4 } { \mathrm { M R } } ^ { 2 }$
D.
$\frac { 5 } { 4 } { \mathrm { M R } } ^ { 2 }$
Q32 Allen 2. MOMENT OF INERTIA MCQ
In the rectangular lamina shown in the figure, AB = BC/2. The moment of inertia of the lamina is minimum along the axis passing through :-
A.
AB
B.
BC
C.
EG
D.
FH
Q33 Allen 2. MOMENT OF INERTIA MCQ
Which of the following bodies of same mass and same radius has minimum moment of inertia ?
A.
Ring
B.
Disc
C.
Hollow sphere
D.
Solid sphere
Q34 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
A ring and a solid sphere of same mass and radius are rotating with the same angular velocity about their diametric axes then :-
A.
it is easier to stop the ring
B.
it is easier to stop the solid sphere
C.
it is equally difficult to stop both of them
D.
it is not possible to stop a rotating body
Q35 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
For rotational motion, the Newton's second law of motion is indicated by :-
A.
$\mathfrak { \omega } _ { 2 } { ^ 2 } = \mathfrak { \omega } _ { 1 } { ^ 2 } + 2 \mathfrak { \alpha } \mathfrak { \theta }$
B.
$\vec { \mathrm { F } } = \frac { \mathrm { d } \vec { \mathrm { p } } } { \mathrm { d t } }$
C.
${ \vec { \tau } } = { \frac { \mathrm { d } { \vec { \mathrm { L } } } } { \mathrm { d t } } }$
D.
$\vec { \mathrm { F } } _ { 1 2 } = \vec { \mathrm { F } } _ { 2 1 }$
Q36 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
In the fig. (a) half of the meter scale is made of wood while the other half of steel. The wooden part is pivoted at O. A force F is applied at the end of steel part. In figure (b) the steel part is pivoted at O' and the same force is applied at the wooden end (In horizontal plane) :-

(a)

(b)
A.
more angular acceleration will be produced in (a)
B.
more angular acceleration will be produced in (b)
C.
same angular acceleration will be produced in both conditions
D.
information is incomplete
Q37 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
The moment of inertia of a disc of radius $0.5,\text{m}$ about its geometric axis is $2,\text{kg}\cdot\text{m}^2$. If a string is tied to its circumference and a force of $10,\text{N}$ is applied, the value of torque with respect to this axis will be:
A.
$2.5,\text{N}\cdot\text{m}$
B.
$5,\text{N}\cdot\text{m}$
C.
$10,\text{N}\cdot\text{m}$
D.
$20,\text{N}\cdot\text{m}$
Q38 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
In the above question, if the disc executes rotatory motion, its angular acceleration will be:
A.
$2.5,\text{rad s}^{-2}$
B.
$5,\text{rad s}^{-2}$
C.
$10,\text{rad s}^{-2}$
D.
$20,\text{rad s}^{-2}$
Q39 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
In the above question, the value of its angular velocity after 2 seconds will be :-
A.
2.5 rad/sec
B.
5 rad/sec
C.
10 rad/sec
D.
20 rad/sec
Q40 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
In the above question, the change in angular momentum of disc in first 2 seconds (in Nm second) will be -
A.
2.5
B.
5
C.
10
D.
20
Q41 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
In the above question, angular displacement of the disc, in first two second will be (in radian) :-
A.
2.5
B.
5
C.
10
D.
20
Q42 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
A particle of mass $m$ and radius of gyration $K$ is rotating with an angular acceleration $\alpha$. The torque acting on the particle is:
A.
$\dfrac{1}{2}mK^2\alpha$
B.
$mK^2\alpha$
C.
$\dfrac{mK^2}{\alpha}$
D.
$\dfrac{1}{4}mK^2\alpha^2$
Q43 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
The grinding stone of a flour mill is rotating at 600 rad/sec. For this, power of 1.2 k watt is used. the effective torque on stone in N–m will be :–
A.
1
B.
2
C.
3
D.
4
Q44 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
A rigid body is rotating about an axis. To stop the rotation, we have to apply :-
A.
pressure
B.
force
C.
momentum
D.
torque
Q45 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
A wheel has moment of inertia $5\times10^{-3},\text{kg m}^2$ and is making $20,\text{rev s}^{-1}$. The torque needed to stop it in $10,\text{s}$ is __________$\times10^{-2},\text{N m}$:
A.
$2\pi$
B.
$2.5\pi$
C.
$4\pi$
D.
$4.5\pi$
Q46 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
A wheel having moment of inertia $2,\text{kg}\cdot\text{m}^2$ about its vertical axis rotates at the rate of $60,\text{rpm}$ about the axis. The torque which can stop the wheel's rotation in one minute would be:
A.
$\dfrac{\pi}{12},\text{N}\cdot\text{m}$
B.
$\dfrac{\pi}{15},\text{N}\cdot\text{m}$
C.
$\dfrac{\pi}{30},\text{N}\cdot\text{m}$
D.
$\dfrac{2\pi}{15},\text{N}\cdot\text{m}$
Q47 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
A constant torque acting on a uniform circular wheel changes its angular momentum from $\mathsf { A } _ { 0 }$ to 4 $\mathrm { A } _ { 0 }$ in 4 seconds. The magnitude of this torque is :–
A.
$\frac { 3 \mathrm { A } _ { 0 } } { 4 }$
B.
$\mathsf { A } _ { 0 }$
C.
$4 \mathrm { A } _ { 0 }$
D.
12 A0
Q48 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
When constant torque is acting on a body then :–
A.
body maintain its state or moves in straight line with same velocity
B.
acquire linear acceleration
C.
acquire angular acceleration
D.
rotates with a constant angular velocity
Q49 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
If torque on a body is zero, then which is conserved:
A.
force
B.
linear momentum
C.
angular momentum
D.
angular impulse
Q50 Allen 3. TORQUE, EQUILIBRIUM OF RIGID BODIES AND TOPPLING MCQ
If I = 50 kg-m2, then how much torque will be applied to stop it in 10 sec. Its initial angular speed is 20 rad/sec. :–
A.
100 N-m
B.
150 N-m
C.
200 N-m
D.
250 N-m