Newton's Second Law: Rotatory Version

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.

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.

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.

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. 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. 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. 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 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.

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