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Rotational Motion

148 Questions Start Allen Test
All Exams Allen Objective Errorless
Q126 Allen 8. PYQ MCQ
The moment of the force, $\vec{F}=4\hat{i}+5\hat{j}-6\hat{k}$ acting at $(2,0,-3)$, about the point $(2,-2,-2)$, is given by:
A.
$-8\hat{i}-4\hat{j}-7\hat{k}$
B.
$-4\hat{i}-\hat{j}-8\hat{k}$
C.
$-7\hat{i}-8\hat{j}-4\hat{k}$
D.
$-7\hat{i}-4\hat{j}-8\hat{k}$
Q127 Allen 8. PYQ MCQ
A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is
A.
7 : 10
B.
5 : 7
C.
10 : 7
D.
2 : 5
Q128 Allen 8. PYQ MCQ
A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere ?
A.
Angular velocity
B.
Moment of inertia
C.
Rotational kinetic energy
D.
Angular momentum
Q129 Allen 8. PYQ MCQ
A disc of radius 2m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it ?
A.
3J
B.
30 kJ
C.
2 J
D.
1 J
Q130 Allen 8. PYQ MCQ
A solid cylinder of mass $2,\text{kg}$ and radius $4,\text{cm}$ is rotating about its axis at the rate of $3,\text{rpm}$. The torque required to stop it after $2\pi$ revolutions is:
A.
$2\times10^{-6},\text{N}\cdot\text{m}$
B.
$2\times10^{-3},\text{N}\cdot\text{m}$
C.
$12\times10^{-4},\text{N}\cdot\text{m}$
D.
$2\times10^{6},\text{N}\cdot\text{m}$
Q131 Allen 8. PYQ MCQ
A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle inclination 30°. The centre of mass of cylinder has speed of 4 m/s. The distance travelled by the cylinder on the incline surface will be : (Take g = 10 m/s2)
A.
2.2 m
B.
1.6 m
C.
1.2 m
D.
2.4 m
Q132 Allen 8. PYQ MCQ
Find the torque about the origin when a force of $3\hat{j},\text{N}$ acts on a particle whose position vector is $2\hat{k},\text{m}$:
A.
$6\hat{k}\text{N}\cdot\text{m}$
B.
$6\hat{i}\text{N}\cdot\text{m}$
C.
$6\hat{j}\text{N}\cdot\text{m}$
D.
$-6\hat{i}\text{N}\cdot\text{m}$
Q133 Allen 8. PYQ MCQ
A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass 'm' is suspended from the rod at 160 cm mark as shown in the figure. Find the value of 'm' such that the rod is in equilibrium. ($g= 10 m/s^2$)
A.
$\frac { 1 } { 2 } \mathrm { k g }$
B.
$\frac { 1 } { 3 } \mathrm { k g }$
C.
$\frac { 1 } { 6 } \mathrm { k g }$
D.
$\frac { 1 } { 1 2 } \mathrm { k g }$
Q134 Allen 8. PYQ MCQ
From a circular ring of mass $M$ and radius $R$, an arc corresponding to a $90^\circ$ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is $KMR^2$. Then the value of $K$ is:
A.
$\dfrac{3}{4}$
B.
$\dfrac{7}{8}$
C.
$\dfrac{1}{4}$
D.
$\dfrac{1}{8}$
Q135 Allen 8. PYQ MCQ
The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the dis about its diameter is :
A.
${ \sqrt { 2 } } : 1$
B.
4 : 1
C.
$1 { : } { \sqrt { 2 } }$
D.
2 : 1
Q136 Allen 8. PYQ MCQ
An energy of $484,\text{J}$ is spent in increasing the speed of a flywheel from $60,\text{rpm}$ to $360,\text{rpm}$. The moment of inertia of the flywheel is:
A.
$0.7\text{kg}\cdot\text{m}^2$
B.
$3.22\text{kg}\cdot\text{m}^2$
C.
$30.8\text{kg}\cdot\text{m}^2$
D.
$0.07\text{kg}\cdot\text{m}^2$
Q137 Allen 8. PYQ MCQ
The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-
A.
${ \sqrt { 5 } } : { \sqrt { 3 } }$
B.
${ \sqrt { 2 } } : { \sqrt { 5 } }$
C.
${ \sqrt { 5 } } : { \sqrt { 2 } }$
D.
${ \sqrt { 3 } } : { \sqrt { 5 } }$
Q138 Allen 8. PYQ MCQ
The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm2. The length of the 400 g rod is nearly :
A.
8.5 cm
B.
17.5 cm
C.
20.7 cm
D.
72.0 cm
Q139 Allen 8. PYQ MCQ
A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is v in the direction shown, which one of the following options is correct (P and Q are any highest and lowest points on the wheel, respectively) ?
A.
Point P moves slower than point Q.
B.
Point P moves faster than point Q.
C.
Both the points P and Q move with equal speed.
D.
Point P has zero speed.
Q140 Allen 8. PYQ MCQ
The radius of gyration of a solid sphere of mass 5 kg about XY is 5m as shown in figure. The radius of the sphere is $\frac { 5 \mathrm { x } } { \sqrt { 7 } } \mathrm { m } .$ , then the value of x is:
A.
5
B.
$\sqrt { 2 }$
C.
$\sqrt { 3 }$
D.
$\sqrt { 5 }$
Q141 Allen 9. ANALYTICAL QUESTIONS MCQ
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Moment of inertia of a particle is a scalar quantity.
Reason (R): Moment of inertia of a particle about any axis is given by $m(\vec{r}\cdot\vec{r})$ where $m$ is mass of particle and $\vec{r}$ is position of particle w.r.t. axis.
In the light of the above statements,
choose the most appropriate answer from the options given below:
A.
Both (A) and (R) are true and (R) is the correct explanation of (A).
B.
Both (A) and (R) are true and (R) is NOT the correct explanation of (A).
C.
(A) is true but (R) is false.
D.
(A) is false but (R) is true.
Q142 Allen 9. ANALYTICAL QUESTIONS MCQ
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Moment of inertia of a disc about an axis perpendicular to its plane passing through its centre is $\dfrac{mR^2}{2}$.
Reason (R): Moment of inertia of a disc about any axis passing through its plane remains equal.
In the light of the above statements,
choose the most appropriate answer from the options given below:
A.
Both (A) and (R) are true and (R) is the correct explanation of (A).
B.
Both (A) and (R) are true and (R) is NOT the correct explanation of (A).
C.
(A) is true but (R) is false.
D.
(A) is false but (R) is true.
Q143 Allen 9. ANALYTICAL QUESTIONS Match the Columns
In diagram axis-3 is perpendicular to plane. Both rods are mass $m$ and length $\ell$ then moment of inertia of system

Image missing
Column-IColumn-II
(i)About axis-1
(ii)About axis-2
(iii)About axis-3
(iv)About axis-4
(P)$\dfrac{m\ell^2}{3}$
(Q)$\dfrac{4m\ell^2}{3}$
(R)$\dfrac{2m\ell^2}{3}$
A.
i – P, ii – Q, iii – R, iv – P
B.
i – Q, ii – Q, iii – R, iv – R
C.
i – R, ii – R, iii – P, iv – Q
D.
i – P, ii – R, iii – Q, iv – P
Q144 Allen 9. ANALYTICAL QUESTIONS Match the Columns
Value of net torque about given points.
Image missing
Column-IColumn-II
(i)Torque about A
(ii)Torque about B
(iii)Torque about C
(iv)Torque about D
(P)$-64\hat{k}$
(Q)$32\hat{k}$
(R)$-12\hat{k}$
(S)$-20\hat{k}$
A.
i – P, ii – Q, iii – R, iv – S
B.
i – Q, ii – R, iii – P, iv – S
C.
i – Q, ii – R, iii – S, iv – P
D.
i – R, ii – S, iii – P, iv – S
Q145 Allen 9. ANALYTICAL QUESTIONS Match the Columns
A particle is projected from point ‘O’ having mass $\cdot _ { \mathrm { m } ^ { \prime } }$ as shown in figure, moving on projectile path

Column-IColumn-II
(i)Torque about O
(ii)Torque about x-axis
(iii)Angular momentum about O
(iv)Angular momentum about x-axis
(P)Zero
(Q)Constant non-zero
(R)Increasing
(S)Decreasing
A.
i – P, ii – Q, iii – R, iv – S
B.
i – R, ii – P, iii – R, iv – P
C.
i – Q, ii – R, iii – R, iv – P
D.
i – P, ii – R, iii – R, iv – S
Q146 Allen 9. ANALYTICAL QUESTIONS Match the Columns
Four identical rods each of mass m and length $\cdot _ { \ell } ,$ are joined to form a rigid square, centre is at origin and sides are parallel to x and y axis then moment of inertia about
Column-IColumn-II
(i)An axis parallel to z-axis and passing through a corner
(ii)One side
(iii)The x-axis
(iv)The z-axis passing through centre
(P)$\frac53m\ell^2$
(Q)$\frac23m\ell^2$
(R)$\frac43m\ell^2$
(S)$\frac103m\ell^2$
A.
i – S, ii – P, iii – Q, iv – R
B.
i – P, ii – Q, iii – R, iv – S
C.
i – Q, ii – R, iii – p, iv – S
D.
i – S, ii – P, iii – R, iv – Q
Q147 Allen 9. ANALYTICAL QUESTIONS MCQ
If lamina is in x-y plane then from theorem of perpendicular axis (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) $\mathrm { I } _ { \mathrm { y } } + \mathrm { I } _ { \mathrm { z } } = \mathrm { I } _ { \mathrm { x } }$
True statements is/are –
A.
B and C
B.
Only D
C.
Only C
D.
C and D
Q148 Allen 9. ANALYTICAL QUESTIONS MCQ
Hinge is smooth and system is released from rest. Select correct statement –

(A) Acceleration of block is g/2 down ward
(B) Acceleration of block is 3g/8 down ward
(C) Tension in string is mg/2
(D) Tension in string is 5mg/8
True statements is/are
A.
A, C
B.
A, D
C.
B, C
D.
B, D