Force Couple

Q. The body under the action and reaction of a force couple undergoes

1. only translational motion
2. only rotational motion
3. both rotational and translational motion
4. None of these

Q. Two balls of masses $m_1=1\text{kg}$ and $m_2=2\text{kg}$ are attached to a massless rod of length $(l=1\text{m})$. Two parallel forces having equal magnitude of $F=1\text{N}$, opposite in direction (couple) are acting on both the balls as shown in the figure. Find the angular acceleration of the system ($\alpha$) about an axis passing through mid-point of the rod and also perpendicular to the plane of the rod. (Take anti-clockwise rotation as +ve)

1. $\frac{2}{3}{\text{rad/s}}^2$
2. $\frac{4}{3}{\text{rad/s}}^2$
3. $\frac{1}{3}{\text{rad/s}}^2$
4. $\frac{1}{6}{\text{rad/s}}^2$

Q. $20\text{Nm}$ torque is applied to a flywheel that rotates about a fixed axis and has moment of inertia of $25{\text{kgm}}^2$. If the flywheel is initially at rest, what is its angular velocity after it has turned through $10$ revolutions?

1. $15\text{rad/s}$
2. $5\text{rad/s}$
3. $20\text{rad/s}$
4. $10\text{rad/s}$

Q. $20\text{Nm}$ torque is applied to a flywheel that rotates about a fixed axis and has moment of inertia of $25{\text{kgm}}^2$. If the flywheel is initially at rest, what is its angular velocity after it has turned through $10$ revolutions?

1. $15\text{rad/s}$
2. $20\text{rad/s}$
3. $5\text{rad/s}$
4. $10\text{rad/s}$

Q. A couple of $10\text{N}$ acting on a rod of length $2\text{m}$ pivoted about its centre $O$ as shown in figure. Find the magnitude of resultant torque acting on rod about point $O$.

1. $10\text{N.m}$
2. $30\text{N.m}$
3. $20\text{N.m}$
4. Can't be determined

Q. The net force of a force couple is

1. Always zero
2. Always non-zero
3. Depends on the distance between the two vectors
4. Depends on the magnitude of the force vectors

Q. The body under the action and reaction of a force couple undergoes

1. only translational motion
2. only rotational motion
3. both rotational and translational motion
4. None of these

Q. The net force of a force couple is

1. Always zero
2. Always non-zero
3. Depends on the distance between the two vectors
4. Depends on the magnitude of the force vectors

Q. A uniform wheel of moment of inertia 'I' is pivoted on a horizontal axis through its centre so that its plane is vertical as shown in the figure. A small mass 'm' is stuck on the rim of the wheel as shown. The angular acceleration of the wheel when mass is at point A is ${\alpha }_A$ and when mass is at point B is ${\alpha }_B$. Then,

1. $\frac{{\alpha }_B}{{\alpha }_A}=\sin \theta$
2. $\frac{{\alpha }_B}{{\alpha }_A}={\sin }^2\theta$
3. $\frac{{\alpha }_B}{{\alpha }_A}=\cos \theta$
4. $\frac{{\alpha }_B}{{\alpha }_A}={\cos }^2\theta$

Q. A uniform solid hemisphere of radius 10 m and mass 64 kg is placed with its curved surface on the smooth horizontal surface and a string AB of length 4 m is attached to point A on its rim as shown in the figure. Find the tension in the string if the hemisphere is in equilibrium.

1. 320 N
2. 640 N
3. 180 N
4. 360 N

Q. A couple is acting on a rigid body,
Statement 1:- Linear acceleration of center of mass of body will be zero
Statement 2:- Magnitude of torque due to couple will be same about any point lying on or outside the body.

1. Statement 1 is correct and statement 2 is incorrect.
2. Statement 1 is incorrect and statement 2 is correct.
3. Both statements are correct.
4. Both statements are incorrect.

Q.

A uniform slender bar AB of mass m is suspended as shown from a small cart of the same mass m. Neglecting the effect of friction, determine the accelerations of points A and B immediately after a horizontal force F has been applied at B

1. $\frac{2F}{5m}$leftwards and $\frac{16F}{5m}$leftwards

2. $\frac{2F}{5m}$rightwards and $\frac{5F}{16}$leftwards

3. $\frac{2F}{m}$rightwards and $\frac{16F}{5m}$leftwards

4. $\frac{2F}{5m}$rightwards and $\frac{16F}{5m}$leftwards