Correlation to Linear Motion

Q. The wheel of a car is rotating at the rate of 1200 revolutions per minute. On pressing the accelerator for 10 seconds, it starts rotating at 4500 revolutions per minute. The angular acceleration of the wheel is

1. $30degrees/se{c}^2$
2. $1880degrees/se{c}^2$
3. $40degrees/se{c}^2$
4. $1980degrees/se{c}^2$

Q. If the position vector of a particle is $\overrightarrow{r}=(3\hat{i}+4\hat{j})$ meter and its angular velocity is $\overrightarrow{\omega }=(\hat{j}+2\hat{k})$ rad/sec then its linear velocity is (in m/s)

1. $(8\hat{i}-6\hat{j}+3\hat{k})$
2. $(3\hat{i}+6\hat{j}+8\hat{k})$
3. -$(3\hat{i}+6\hat{j}+6\hat{k})$
4. $(6\hat{i}+8\hat{j}+3\hat{k})$

Q. A wheel is performing combined translational and rotational motion on a frictionless horizontal surface on a truck which is moving with a constant linear velocity $v=10\text{m/s}$. Centre of the wheel is also moving with a constant linear velocity $v=10\text{m/s}$ with respect to ground. The wheel is rotating with angular velocity $\omega =2\text{rad/s}$. Find velocity of point $A$ (Which is the topmost point of wheel as shown in the figure) with respect to ground. Radius of the wheel is $1\text{m}$.

1. $10\hat{i}$
2. $8\hat{i}$
3. $6\hat{i}$
4. zero

Q. A particle is sticked to a disc at a distance $\frac{r}{2}\text{m}$ from centre. Disc has initial angular velocity of ${\omega }_o=6\hat{j}\text{rad/s}$ and constant angular acceleration of $\alpha =-\hat{j}{\text{rad/s}}^2$ as shown in figure. If radius of disc is $1\text{m}$, find the speed of particle after $t=2\text{s}$.

1. $4\text{m/s}$
2. $3\text{m/s}$
3. $6\text{m/s}$
4. $2\text{m/s}$

Q. A pendulum is suspended from a point $A$ and is given a small initial velocity so that it starts oscillating. What will be the axis of rotation for this oscillating pendulum?

1. A line passing through $A$ on the plane of oscillation.
2. A line passing through the bob of the pendulum, perpendicular to the plane of oscillation.
3. A line along the rod of the pendulum n the plane of oscillation.
4. A line passing through $A$, perpendicular to the plane of oscillation.

Q. Paragraph for below question
नीचे दिए गए प्रश्न के लिए अनुच्छेद

Velocities of end points of a uniform rod of mass M and length L is shown in figure. Then

M द्रव्यमान व L लम्बाई की एकसमान छड़ के सिरों के वेग चित्रानुसार हैं। तब


Q. Velocity of centre of mass of rod is

प्रश्न -छड़ के द्रव्यमान केन्द्र का वेग है

1. 2v₀
   
2. 3v₀
   
3. $\frac{3}{2}{v}_0$
   
4. 4v₀
   

Q. A disc is having an initial angular velocity of $4\text{rad/sec}$ and angular acceleration of $8{\text{rad/sec}}^2$. Find the angle rotated (in radian) by disc in $3\text{sec}$.

1. $48\text{rad}$
2. $36\text{rad}$
3. $12\text{rad}$
4. $24\text{rad}$

Q. The centre of mass of a uniform rod of length $10\text{m}$ is moving with translational velocity of $50\text{m/s}$ on a frictionless horizontal surface as shown in the figure and the rod rotates about its centre of mass with an angular velocity of $5\text{rad/sec}$. Find out the velocities of points $A$ and $B$.

1. $\overrightarrow{V_A}=75\hat{i}$
2. $\overrightarrow{V_B}=25\hat{i}$
3. $\overrightarrow{V_A}=25\hat{i}$
4. $\overrightarrow{V_B}=75\hat{i}$

Q.

A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 seconds. Find the angular acceleration.

1. $50\frac{rev}{s^2}$

2. $25\frac{rev}{s^2}$

3. $40\frac{rev}{s^2}$

4. $500\pi \frac{radians}{s^2}$

Q. Which of the following is an example of rotational motion?
$i)$ Motion of an electron around the nucleus.
$ii)$ Motion of the cap of a water bottle when it is being opened.
$iii)$ Motion of a fan.
$iv)$ Motion of the clothes inside a washing machine.
$v)$ A vehicle moving along the circumference of a circle

1. $\left(i\right),\left(iii\right)$ and $\left(v\right)$
2. $\left(i\right)$ and $\left(iv\right)$
3. $\left(ii\right)$ and $\left(iii\right)$
4. $\left(ii\right)$ and $\left(iv\right)$

Q.

Find the time period of meeting of minute hand and second hand of a clock.

1. $t$ = $\frac{59}{60}$min.

2. $t$ = $\frac{60}{59}$min.

3. $t$ = 59 min

4. $t$ = 60 min

Q. A motorcycle is moving with speed $20\text{m/s}$ on the road. The M.O.I of wheel about its axis of rotation is $2{\text{kg m}}^2$ and radius of its wheel is $0.5\text{m}$. Motorcycle comes to rest in $10\text{sec}$ after applying the brake. Find the magnitude of the average torque transmitted by its brake to the wheel?

1. $8{\text{kg m}}^2{\text{/s}}^2$
2. $16{\text{kg m}}^2{\text{/s}}^2$
3. $4{\text{kg m}}^2{\text{/s}}^2$
4. $2{\text{kg m}}^2{\text{/s}}^2$

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

A uniform rod (m, l) is supported with the help of two strings as shown. At equilibrium let tension in string 1 and string 2 be T₁ and T₂ respectively, then

एक समरूप छड़ (m, l) दर्शाए अनुसार दो डोरियों द्वारा आधारित है। साम्य पर, माना डोरी 1 व डोरी 2 में तनाव क्रमशः T₁ व T₂ हैं, तब

1. $T_1=\frac{mg}{3}$
2. $T_2=\frac{2mg}{3}$
3. 2T₁ = T₂
4. 2T₂ = T₁

Q. Angular displacement $\theta$ of a flywheel varies with time as $\theta =at+b{t}^2+c{t}^3$, then angular acceleration of the flywheel is given by

1. $a+2bt-3c{t}^2$
2. $2b-6t$
3. $a+2b-6t$
4. $2b+6ct$

Q. A particle is sticked to a disc at a distance $\frac{r}{2}\text{m}$ from centre. Disc has initial angular velocity of ${\omega }_o=6\hat{j}\text{rad/s}$ and constant angular acceleration of $\alpha =-\hat{j}{\text{rad/s}}^2$ as shown in figure. If radius of disc is $1\text{m}$, find the speed of particle after $t=2\text{s}$.

1. $4\text{m/s}$
2. $3\text{m/s}$
3. $6\text{m/s}$
4. $2\text{m/s}$

Q.

A disc rotates about its axis with a constant angular acceleration of 4 $\frac{rad}{s^2}$. Find the radial and tangential accelerations of a particle at a distance of 1 cm from the axis at the end of the first second after the disc starts rotating.

1. $16\frac{cm}{s^2},4\frac{cm}{s^2}$

2. $0.16\frac{cm}{s^2},0.04\frac{cm}{s^2}$
3. $16\frac{m}{s^2},4\frac{m}{s^2}$
4. $1.6\frac{cm}{s^2},0.4\frac{cm}{s^2}$

Q. The relative distances between the particles of a body $A$ is fixed and does not change. Which of the following statements about the body is wrong?

1. The body undergoes negligible deformation.
2. Body is elastic.
3. The body is perfectly rigid
4. A force acting on the body does not change its structure

Q. A wheel of radius $1\text{m}$ is performing combined translational and rotational motion on a frictionless horizontal surface with an angular velocity $4\text{rad/s}$ and translational velocity of its COM is $V_0=10\text{m/s}$ as shown in figure. Find the magnitude of velocity of point $P$, if the line $OP$ makes angle ${30}^{\circ }$ with the horizontal.

1. $10\text{m/s}$
2. $4\text{m/s}$
3. $2\sqrt{39}\text{m/s}$
4. $4\sqrt{39}\text{m/s}$

Q. A disc is having an initial angular velocity of $4\text{rad/sec}$ and angular acceleration of $8{\text{rad/sec}}^2$. Find the angle rotated (in radian) by disc in $3\text{sec}$.

1. $48\text{rad}$
2. $36\text{rad}$
3. $12\text{rad}$
4. $24\text{rad}$

Q.

What is a rigid body?

Q. A wheel starting with angular velocity of $10\text{rad/sec}$ acquires angular velocity of $100\text{rad/sec}$ in $15\text{seconds}$. If angular acceleration of wheel is constant, what will be the angular displacement of a point on the wheel in $15\text{seconds}$?

1. $820\text{rad}$
2. $825\text{rad}$
3. $675\text{rad}$
4. $150\text{rad}$

Q. The angular distance (θ), the radius (r), and the linear distance (d) is related as

1. d=2rθ
2. d=r/θ
3. d=rθ
4. d=1/2rθ

Q. A disc having radius $r=1\text{m}$ and $m=2\text{kg}$ is rotating about an axis passing through its COM and perpendicular to the plane of disc. Initial velocity of a point $A$ at the edge of disc is $6\text{m/s}$. A retarding torque of magnitude $2\text{Nm}$ starts acting on disc about its axis of rotation. Find the velocity of point $A$ after $t=2\text{s}$.

1. $1\text{m/s}$
2. $3\text{m/s}$
3. $4\text{m/s}$
4. $2\text{m/s}$

Q. A wheel has initial angular speed of $\pi \text{rad/s}$. A constant force is acting on wheel to stop it. If wheel covers $\theta =\frac{\pi }{2}\text{rad}$ before coming to rest, find the magnitude of angular acceleration of the wheel.

1. $\frac{\pi }{2}{\text{rad/s}}^2$
2. $\frac{\pi }{3}{\text{rad/s}}^2$
3. $\pi {\text{rad/s}}^2$
4. $\frac{\pi }{4}{\text{rad/s}}^2$