Rotational Motion — DPP 3

20 NEET questions from Rotational Motion, with answers and explanations. Attempt it as a timed test to get scoring, accuracy breakdown and mistake tracking.

Attempt this test free 20 questions · 30 minutes · +80 marks
1
A stone attached to one end of string is revolved around a stick so that the string winds upon the stick and gets shortened. What is conserved?
  1. A angular momentum
  2. B linear momentum
  3. C kinetic energy
  4. D none of the above
Show answer & explanation

Correct answer: A

Since torque of string on stone is zero, the angular momentum will be conserved.
2
In the above question, the angular velocity will :-
  1. A increase
  2. B decrease
  3. C not change
  4. D nothing can be said
Show answer & explanation

Correct answer: B

Iω = constant
I ↑ ω ↓
3
A force $\overrightarrow { \mathrm { F } } = 2 \hat { \mathrm { i } } - 3 \hat { \mathrm { k } }$ acts on a particle at $\overrightarrow { \mathrm { r } } = 0.5 \hat { \mathrm { j } } - 2 \hat { \mathrm { k } }$. The torque $\tau$ acting on the particle relative to a point with co-ordinates (2.0 m, 0, -3.0 m) is
  1. A $( - 3.0 \hat { \mathrm { i } } - 4.5 \hat { \mathrm { j } } - \hat { \mathrm { k } } ) \mathrm { N } - \mathrm { m }$
  2. B $( 3 \hat { \mathrm { i } } + 6 \hat { \mathrm { j } } - \hat { \mathrm { k } } ) \mathrm { N } - \mathrm { m }$
  3. C $( - 20 \hat { \mathrm { i } } + 4.0 \hat { \mathrm { j } } + \hat { \mathrm { k } } ) \mathrm { N } - \mathrm { m }$
  4. D $( - 1.5 \hat { \mathrm { i } } - 4.0 \hat { \mathrm { j } } - \hat { \mathrm { k } } ) \mathrm { N } - \mathrm { m }$
Show answer & explanation

Correct answer: D

Rotational Motion – NEET-7141
4
What is the moment of inertia of ring about its diameter?
  1. A MR$^{2}$
  2. B $\frac { \mathrm { MR } ^ { 2 } } { 2 }$
  3. C $\frac { 3 } { 4 } M R ^ { 2 }$
  4. D $\frac { 5 } { 4 } M R ^ { 2 }$
Show answer & explanation

Correct answer: B

Along diameter in the plane.
Rotational Motion – NEET-7099 Using Axis theorem
$\begin{array}{l}\mathrm{I}_{\mathrm{x}}+\mathrm{I}_{\mathrm{y}}=\mathrm{I}_{\mathrm{z}} \\ 2 \mathrm{I}_{\mathrm{x}}=\mathrm{I}_{\mathrm{z}} \\ \mathrm{I}_{\mathrm{x}}=\frac{\mathrm{MR}^{2}}{2}\end{array}$
5
Four particles each of mass m are placed at the corners of a square of side length $\ell$. The radius of gyration of the system about an axis perpendicular to the square and passing through centre is :-
  1. A $\frac { \ell } { \sqrt { 2 } }$
  2. B $\frac { \ell } { 2 }$
  3. C $\ell$
  4. D $\ell \sqrt { 2 }$
Show answer & explanation

Correct answer: A

Rotational Motion – NEET-7090
6
Which of the following bodies of same mass and same radius has minimum moment of inertia?
  1. A Ring
  2. B Disc
  3. C Hollow sphere
  4. D Solid sphere
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Correct answer: D

$\begin{array}{l}\mathrm{I}_{\mathrm{R}}=\mathrm{MR}^{2}, \mathrm{I}_{\mathrm{D}}=\mathrm{MR}^{2} / 2 \\ \mathrm{I}_{\mathrm{HS}}=\frac{2}{3} \mathrm{MR}^{2} \mathrm{I}_{\mathrm{SS}}=\frac{2}{5} \mathrm{MR}^{2}\end{array}$
7
On melting of ice on the pole of the earth, its moment of inertia will :-
  1. A increase
  2. B decrease
  3. C remain unchanged
  4. D none of these
Show answer & explanation

Correct answer: A

On melting water will be more at equator which increase "r",
∴ moment of inertia increases.
8
A person is standing on the edge of a circular platform, which is moving with constant angular speed about an axis passing through its centre and perpendicular to the plane of platform. If person is moving along any radius towards axis of rotation then the angular velocity will :-
  1. A decrease
  2. B remain unchanged
  3. C increase
  4. D data is insufficient
Show answer & explanation

Correct answer: C

As person is coming towards axis, it's distance from axis decreases.
So M.I also decreases.
From conservation of angular momentum :- as I decreases so, ω increases
9
Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momentum will be in the ratio :-
  1. A 1 : 2
  2. B $\sqrt { 2 } : 1$
  3. C $1 : \sqrt { 2 }$
  4. D 2 : 1
Show answer & explanation

Correct answer: C

Relation between, kinetic energy (K) and angular momentum (L) is :-
$\begin{array}{l}\mathrm{L}=\sqrt{2 \mathrm{IK}} \quad\{\text { where, } \mathrm{I}=\text { moment of inertia }\} \\ \text { so, } \quad \frac{\mathrm{L}_{1}}{\mathrm{~L}_{2}}=\sqrt{\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}}=\sqrt{\frac{\mathrm{I}}{2 \mathrm{I}}}=1: \sqrt{2}\end{array}$
10
A particle of mass $m$ is rotating in a plane in a circular path of radius r. Its angular momentum is L. The centripetal force acting on the particle is
  1. A $\frac { L ^ { 2 } } { m r }$
  2. B $\frac { L ^ { 2 } m } { r }$
  3. C $\frac { \mathrm { L } ^ { 2 } } { \mathrm { mr } ^ { 2 } }$
  4. D $\frac { \mathrm { L } ^ { 2 } } { \mathrm { mr } ^ { 3 } }$
Show answer & explanation

Correct answer: D

Rotational Motion – NEET-7178
11
A ring of mass 10 kg and diameter 0.4 meter is rotating about its geometrical axis at 1200 rotations per minute. Its moment of inertia and angular momentum will be respectively:-
  1. A $0.4 \mathrm {~kg} - \mathrm { m } ^ { 2 }$ and $50.28 \mathrm {~J} - \mathrm { s }$
  2. B $0.4 \mathrm {~kg} - \mathrm { m } ^ { 2 }$ and $0.4 \mathrm {~J} - \mathrm { s }$
  3. C $50.28 \mathrm {~kg} - \mathrm { m } ^ { 2 }$ and $0.4 \mathrm {~J} - \mathrm { s }$
  4. D $0.4 \mathrm {~kg} - \mathrm { m } ^ { 2 }$ and zero
Show answer & explanation

Correct answer: A

Rotational Motion – NEET-7169
12
If the earth loses its atmosphere suddenly, then the duration of day will :-
  1. A increase
  2. B decrease
  3. C remain unchanged
  4. D nothing can be definitely said
Show answer & explanation

Correct answer: B

On loosing atmosphere, moment of inertia of earth decreases so, ω increases and time period T decreases.
$\left\{\because \mathrm{T}=\frac{2 \pi}{\omega}\right\}$
13
The rotational kinetic energy of a body is K$_{rot}$ and its moment of inertia is I. The angular momentum of body is
  1. A $\mathrm { IK } _ { \text {rot } }$
  2. B $2 \sqrt { \text { IK } _ { \text {rot } } }$
  3. C $\sqrt { 2 \mathrm { IK } _ { \mathrm { rot } } }$
  4. D $2 \mathrm { IK } _ { \text {rot } }$
Show answer & explanation

Correct answer: C

Rotational kinetic energy of a body,
$\begin{array}{l}K_{\mathrm{rot}}=\frac{1}{2} I \omega^{2} \\ \text { or, } I \omega^{2}=2 K_{\mathrm{rot}} \text { or } \omega=\sqrt{\frac{2 K_{\mathrm{rot}}}{I}}\end{array}$
Angular momentum of a body L = Iω
or, $\mathrm{L}=\mathrm{I} \sqrt{\frac{2 \mathrm{~K}_{\mathrm{rot}}}{\mathrm{I}}}=\sqrt{2 \mathrm{IK}_{\mathrm{rot}}}$ [From (i)]
14
The rotational kinetic energy of two bodies of moments of inertia 9 kg-m$^{2}$ and 1 kg-m$^{2}$ are same. The ratio of their angular momentum is :-
  1. A 3 : 1
  2. B 1 : 3
  3. C 9 : 1
  4. D 1 : 9
Show answer & explanation

Correct answer: A

Rotational Motion – NEET-7170
15
For rotational motion, the Newton's second law of motion is indicated by :-
  1. A $\omega _ { 2 } { } ^ { 2 } = \omega _ { 1 } { } ^ { 2 } + 2 \alpha \theta$
  2. B $\vec { F } = \frac { d \vec { p } } { d t }$
  3. C $\vec { \tau } = \frac { d \vec { L } } { d t }$
  4. D $\vec { F } _ { 12 } = \vec { F } _ { 21 }$
Show answer & explanation

Correct answer: C

$\begin{array}{l}\vec{\tau}=I \vec{\alpha} \text { like } \vec{F}=m \vec{a} \\ \vec{\tau}=\frac{d \vec{L}}{d t} \text { like } \vec{F}=\frac{d \vec{p}}{d t}\end{array}$
16
A round disc of moment of inertia I$_{2}$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I$_{1}$ rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of discs is :-
  1. A ω
  2. B $\frac { I _ { 1 } \omega } { I _ { 1 } + I _ { 2 } }$
  3. C $\frac { \left( I _ { 1 } + I _ { 2 } \right) \omega } { I _ { 1 } }$
  4. D $\frac { I _ { 2 } \omega } { I _ { 1 } + I _ { 2 } }$
Show answer & explanation

Correct answer: B

Applying conservation of angular momentum
$\begin{array}{l}I_{1} \omega=\left(I_{1}+I_{2}\right) \omega^{\prime} \\ \text { so, } \quad \omega^{\prime}=\frac{I_{1} \omega}{\left(I_{1}+I_{2}\right)}\end{array}$
17
In the above question, the value of its angular velocity after 2 seconds will be :-
  1. A 2.5 rad/sec
  2. B 5 rad/sec
  3. C 10 rad/sec
  4. D 20 rad/sec
Show answer & explanation

Correct answer: B

$\begin{array}{l}\omega=\omega_{0}+\alpha t \\ \Rightarrow \quad \omega=0+2.5 \times 2=5 \mathrm{rad} / \mathrm{sec}\end{array}$
18
A wheel is rotating about its axis at a constant angular velocity. If suddenly an object sticks to it on the rim, then its M.I. will :-
  1. A increase
  2. B decrease
  3. C remain unchanged
  4. D nothing can be said
Show answer & explanation

Correct answer: A

m ↑ I ↑
19
In the above question, the change in angular momentum of disc in first 2 seconds (in Nm second) will be -
  1. A 2.5
  2. B 5
  3. C 10
  4. D 20
Show answer & explanation

Correct answer: C

$\begin{array}{l}\text { as, } \quad \tau=\frac{\Delta \mathrm{L}}{\Delta \mathrm{t}} \\ \text { so, } \Delta \mathrm{L}=\tau \times \Delta \mathrm{t} \\ \Rightarrow \quad \Delta \mathrm{L}=\text { change in angular momentum }=5 \times 2 \\ =10 \mathrm{~N} \text {-m sec }\end{array}$
20
In Figure (a), half of the meter scale is made of wood, while the other half is of steel. The wooden part is pivoted at O. A force F is applied at the end of the steel part. In figure (b), the steel part is pivoted at O', and the same force is applied at the wooden end (in the horizontal plane) :-
Rotational Motion – NEET-7123
  1. A more angular acceleration will be produced in (a)
  2. B more angular acceleration will be produced in (b)
  3. C same angular acceleration will be produced in both conditions
  4. D information is incomplete
Show answer & explanation

Correct answer: B

Angular acceleration will be more if M.I will be less.
$(\vec{\tau}=I \vec{\alpha})$

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