Newton's Second Law: Rotatory Version

Q.

The rotational analogue of force is :

Q. A fly wheel of moment of inertia $3\times {10}^{2}kg{m}^2$ is rotating with uniform angular speed of 4.6 $rad{s}^{-1}.$ If a torque of $6.9\times {10}^2$ Nm retards the wheel, then the time in which the wheel comes to rest is

1. 1.5 s
2. 2 s
3. 0.5 s
4. 1 s
5. 2.5 s

Q.

A uniform solid cylinder of mass 'M' and radius 'R' is resting on a horizontal platform (which is parallel to X-Y plane) with its axis along the Y-axis and free to roll on the platform. The platform is given a motion in X-direction given by $x=A\cos \omega t$. There is no slipping between the cylinder and the platform. The maximum torque acting on the cylinder as measured about its centre of mass is

1. $\frac{1}{2}MRA{\omega }^2$
2. $mRA\omega A^2{\cos }^2\omega t$
3. $MRA{\omega }^2$
4. $2mRA{\omega }^2$

Q.

A hollow sphere of radius 'R' rests on a horizontal surface of finite coefficient of friction. A point object of mass 'm' moved horizontally and hits the sphere at a height of 'R/2' above its center. The collision is instantaneous and completely inelastic. Which of the following is/are correct ?

1. Total linear momentum of the system is not conserved
2. Total angular momentum about center of mass of the system remains conserved

3. The sphere gets finite angular velocity immediately after collision

4. The sphere moves with finite speed immediately after collision

Q. The torque $\overrightarrow{\tau }$ on a body about a given point is found to be $\overrightarrow{A}\times \overrightarrow{L}$ where $\overrightarrow{A}$ is a constant vector and $\overrightarrow{L}$ is angular momentum of the body about that point. From this it follows that

1. $\frac{d\overrightarrow{L}}{dt}$ is perpendicular to $\overrightarrow{L}$ at all times.

2. the magnitude of $\overrightarrow{L}$ does change with time.

3. $\overrightarrow{L}$ does not change with time.

4. the component of $\overrightarrow{L}$ in the direction of $\overrightarrow{A}$ does change with time.

Q.

Which of the following quantities measured from different inertial reference frames are the same?

1. Force

2. Velocity

3. Displacement

4. Kinetic energy

Q.

A constant force 'F' is applied at the top of a ring as shown in figure. Mass of the ring is 'M' and radius is 'R'. Angular momentum of particle about point of contact at time 't' is

1. Is Zero
2. Decreases linearly with time
3. Is constant
4. Increases linearly with time

Q.

When you drop a ball you find that the ball accelerates towards the Earth due to the mutual gravitational force experienced. By Newton’s third law, the Earth also should experience an equal and opposite force. Why do we not see the Earth accelerating towards the ball?

Q. A centrifuge consists of four solid cylindrical containers, each of mass 'm' at radial distance 'r' from the axis of rotation. A time 't' is required to bring the centrifuge to an angular velocity $\omega$ from rest under a constant torque $\tau$ applied to the shaft. The radius of each container is 'a' and the mass of the shaft and the supporting arms is small compared to 'm'. Then

1. $t=\frac{4m{r}^2\omega }{\tau }$
2. $t=\frac{2m(r^2+2a^2)\omega }{\tau }$
3. $t=\frac{2m(a^2+2r^2)\omega }{\tau }$
4. $t=\frac{2m{a}^2\omega }{\tau }$

Q. A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

1. $\frac{2g}{2L}$
2. $\frac{2g}{L}$
3. $\frac{3g}{2L}$
4. $\frac{g}{L}$

Q. The net torque on a rigid body due to its internal forces is always?

1. Zero
2. Maybe Zero.
3. Non-Zero
4. None of these

Q.

Point P is $\overrightarrow{r}$ away from O and a force $\overrightarrow{F}$ is applied at P as shown.

What can be said about $\overrightarrow{T}$ of $\overrightarrow{F}$ about O ?

1. $\overrightarrow{T}$ $\perp$ $\overrightarrow{F}$ and $\overrightarrow{T}$ || $\overrightarrow{r}$

2. $\overrightarrow{T}$ $\perp$ $\overrightarrow{F}$ and is directed outside the plane containing $\overrightarrow{T}$ $\perp$ $\overrightarrow{F}$ and $\overrightarrow{r}$ and $\overrightarrow{F}$

3. $\overrightarrow{T}$ || $\overrightarrow{F}$ and $\overrightarrow{T}$ $\perp$ $\overrightarrow{r}$

4. $\overrightarrow{T}$ $\perp$ $\overrightarrow{F}$ and $\overrightarrow{T}$ $\perp$ $\overrightarrow{r}$
   and is directed inside the plane containing $\overrightarrow{r}$ and $\overrightarrow{F}$

Q. A ring of radius 1m has moment of inertia of $10kg-m^2$ about an axis through its centre and perpendicular to its plane. If a constant force of 50N is applied to it tangentially as shown, what will be its angular acceleration?

1. $2.5rad/s^2$
2. $5rad/s^2$
3. $\pi rad/s^2$
4. $10rad/s^2$

Q.

If net external force on a body adds up to zero, which of the following statements are not necessarily true?

1. Net External torque about any point need not be zero

2. Linear acceleration of the centre of mass is zero

3. Angular acceleration of the body has to be zero

4. Angular momentum about any axis may not be conserved

Q.

If the line of action of the applied force intersects the Axis of rotation, then the torque of this force about the axis of rotation is

1. Always zero

2. Sometime non-zero

3. Always non-zero perpendicular to the axis of rotation

4. Non-zero and along the axis of rotation

Q. A door can just be opened with $10N$ force on the handle of the door. The handle is at a distance of $50cm$ from the hinges. Then the torque applied on the door is ( in $Nm$ ):

1. $5$
2. $10$
3. $15$
4. $20$

Q. A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed $\omega$, as shown int he figure. At time t = 0, a small insect starts from O and moves with constant speed v with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains $\omega$ throughout. The magnitude of the torque $\left(\overrightarrow{\tau }\right)$ on the system about O, as a function of time is best represented by which plot?

1. 
2. 
3. 
4. 

Q.

The torque of force about a line is dependent of the choice of the origin which lies on that line itself.

1. False

2. True

Q.

Which of the following are the necessary and sufficient conditions for a body to have some angular acceleration about a fixed Axis?

1. Net external force is non-zero

2. Net external torque is non-zero

3. Net external torque is zero

4. Angular momentum is not conserved

Q.

Which of following rotational physical quantities do not match to given translational analogies?

1. Angular velocity-linear velocity

2. Angular displacement - linear displacement

3. Torque - Kinetic Energy

4. Moment of Inertia - mass

Q.

Which of the following cases, a rigid body, necessarily has an angular acceleration.

1. Line of action of force is parallel to Axis of rotation

2. Line of action of force is perpendicular to the axis of rotation

3. Line of action of the force is perpendicular and skew to the Axis of rotation

4. Line of action of the force intersects the axis of rotation

Q. The roller of diameter 0.6 m has to be raised on the pavement XY by forces $F_1$ and $F_2$ each of magnitude 15 N. The ratio of torques produced by the two forces is __________​.

1. 1:3
2. 1:2​
3. 3:1​
4. 2:1