Correlation to Linear Motion

Q. The time period of a simple pendulum is $T$. The time taken to complete $5/8$ oscillation starting from mean position is $\frac{\alpha }{12}T$. The value of $\alpha$ is _______.

Q.

What is center of oscillation?

Q. A particle is moving on a circular path of 10 m radius. At any instant of time, its speed is 5 m/s and the speed is increasing at a rate of $2m/s^2$. The magnitude of net acceleration at this instant is:

1. $5m/s^2$
2. $2m/s^2$
3. $3.2m/s^2$
4. $4.3m/s^2$

Q. Select the correct option about rigid body.

1. Shape and size of the body remains the same.
2. All the above are correct.
3. No change in the distance between any pair of particles.
4. No velocity of seperation or approach between any pair of particles.

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. 

2. 

3. 

4. 

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 passing through $A$, perpendicular to the plane of oscillation.
4. A line along the rod of the pendulum n the plane of oscillation.

Q. When a person throws a meter stick, it is found that the centre of the stick is moving with a speed of $10\text{m/s}$ vertically upward & the left end of the stick with a speed $20\text{m/s}$ vertically upward. Then, the angular speed of the stick is

1. $20\text{rad/sec}$
2. $10\text{rad/sec}$
3. $30\text{rad/sec}$
4. None of the these

Q.

A wheel rotation with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.

Q.

Angular velocities of two bodies rotating in same direction are given by ${\omega }_1$ = 30 rad/sec. ${\omega }_2$ = 60 rad/sec, the relative angular velocity of $2^{nd}$ body with respect to $1^{st}$ body is

1. 30 rad/sec

2. 40 rad/sec

3. 50 rad/sec

4. 60 rad/sec

Q. A wheel rotating at a speed of $600\text{rpm}$ (revolutions per minute) about its axis is brought to rest by applying a constant torque for $10$ seconds. The angular velocity $5$ seconds after the application of the torque is $n\pi \text{rad/s}$ where $n$ is

1. $1$
2. $10$
3. $5$
4. $20$

Q.

A bullet fired into a fixed wooden block loses half of its velocity after penetrating $40cm$. It comes to rest after penetrating a further distance of

1. $\frac{40}{3}cm$

2. $\frac{20}{3}cm$

3. $\frac{22}{5}cm$

4. $\frac{26}{5}cm$

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 boat's propeller has a rotational inertia of $4{\text{kg-m}}^2$. After a constant torque is applied for $12\text{s}$, the propeller's angular speed changes from a clockwise $8\text{rad/s}$ to counter-clock wise $8\text{rad/s}$. What was the torque applied to the propeller?

1. $4.3\text{N-m}$
2. $5.3\text{N-m}$
3. $6.3\text{N-m}$
4. $7.3\text{N-m}$

Q.

A motorcycle has to move with a constant speed on an overbridge which is in the form of a circular arc of radius R and has a total length L. Suppose the motorcycle starts from the highest point. (a) What can its maximum velocity be for which the contact with the road is not broken at the highest point ? (b) If the motorcycle goes at speed $\frac{1}{\sqrt{2}}$ times the maximum found in part (a), where will it lose the contact with the road ? (c) What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge ?

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

Q. A uniform disc rotating with constant angular acceleration covers $50$ revolutions in the first five seconds after it starts from rest. Calculate the angular acceleration.

1. $4{\text{rev/s}}^2$
2. $2{\text{rev/s}}^2$
3. $8\pi {\text{rev/s}}^2$
4. $4\pi {\text{rev/s}}^2$

Q.

A particle travels in a circle of radius 20 $cm$ at a speed that uniformly increases. If the speed changes form 5.0 $\frac{m}{s}$ to 6.0 $\frac{m}{s}$ in 2.0 $s$, find the angular acceleration.

1. 2.5

2. 5 rad/s²

3. 7.5

4. 6

Q. A fan initially rotating at $60\text{rad/sec}$ clockwise accelerates and aquires an angular velocity of $110\text{rad/sec}$ clockwise. If the angular acceleration of fan is constant and it takes $2\text{sec}$ to change its angular velocity, find the angular acceleration of the fan.

1. $50{\text{rad/sec}}^2$ in counterclockwise direction.
2. $25{\text{rad/sec}}^2$ in counterclockwise direction.
3. $25{\text{rad/sec}}^2$ in clockwise direction.
4. $50{\text{rad/sec}}^2$ in clockwise direction.

Q. A solid sphere of mass $m$ and radius $R$ is gently placed on a conveyer belt moving with constant velocity $V_0$. If coefficient of friction between belt and sphere is $2/7$, the distance travelled by the centre of the sphere before it starts pure rolling is

1. $\frac{V_0^2}{7g}$
   
2. $\frac{2V_0^2}{49g}$
3. $\frac{2V_0^2}{5g}$
4. $\frac{2V_0^2}{7g}$

Q.

What is minimum orbital velocity?

Q.

Why we use Katers pendulum

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. $\left(ii\right)$ and $\left(iii\right)$
3. $\left(i\right)$ and $\left(iv\right)$
4. $\left(ii\right)$ and $\left(iv\right)$

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

Q.

The height$\mathrm{y}$ and the distance $\mathrm{x}$along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $\mathrm{y}=(8\mathrm{t}-5{\mathrm{t}}^2)\mathrm{m}\mathrm{and}\mathrm{x}=6\mathrm{t}\mathrm{m},$ where t is in seconds. The velocity with which the projectile is projected at $\mathrm{t}=0$ is.?

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.

A solid body starts rotating about a stationary axis with an angular acceleration $alpha$ = $at$. How soon after the beginning of rotation will the total acceleration vector of an arbitrary point of the body form an angle = ${60}^{\circ }$ with its velocity vector?

1. 

2. 

3. 

4. 

Q. A sphere is rotating uniformly about a fixed axis passing though its centre. Then,

1. The particles in the sphere do not have any angular acceleration.
2. The particles on the axis do not have any linear acceleration.
3. Different particles in the sphere have the same angular speeds.
4. All the particles in the sphere have the same linear speed.

Q.

7. What is a rigid body?

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 $A$ with respect to ground. Radius of the wheel is $1\text{m}$.

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

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