Force Couple

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 small block is connected to a massless rod, which in turn is attached to a spring of force constant k as shown in fig. The block is displaced down slightly, and left free.

1. $2\pi \left(\frac{b}{a}\right)\sqrt{\frac{m}{k}}$
2. $2\pi \left(\frac{a}{b}\right)\sqrt{\frac{m}{k}}$
   
3. $2\pi \left(\frac{b}{a}\right)\sqrt{\frac{k}{m}}$
   
4. $2\pi \left(\frac{a}{b}\right)\sqrt{\frac{k}{m}}$

Q. A wheel of radius $20\text{cm}$ has four forces applied to it, as shown in the figure. The total torque produced by these forces about centre $O$ is

1. $5.4\text{N-m},\text{Anticlockwise}$
2. $1.8\text{N-m},\text{Clockwise}$
3. $1.8\text{N-m},\text{Anticlockwise}$
4. $5.4\text{N-m},\text{Clockwise}$

Q. Four point masses, each of mass $m$ are fixed at the corners of a square of side $l$. The square is rotating with angular frequency $\omega$, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is:

1. $m{l}^2\omega$
2. $4m{l}^2\omega$
3. $3m{l}^2\omega$
4. $2m{l}^2\omega$

Q. A couple consisting of two forces $F_1$ and $F_2$ each equal to $5\text{N}$ is acting at the rim of a disc of mass $2\text{kg}$ and radius $0.5\text{m}$ for $5\text{s}$. Initially, the disc is at rest, the final angular momentum of the disc is

1. $20\text{Nm-s}$
2. $15\text{Nm-s}$
3. $25\text{Nm-s}$
4. $30\text{Nm-s}$

Q.

A meter scale is kept on a knife edge at $50cm$ mark. A weight of $20gf$ is hanging at $80cm$ mark and a weight of $50gf$ is hanging at $60cm$ mark . Where should a weight of $55gf$ be placed to make the meter scale balanced?

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. A rectangular solid box of length $0.3\text{m}$ is held horizontally, with one of its sides on the edge of a platform of height $5\text{m}$. When released, it slips off the table in a very short time $\tau =0.01\text{s}$, remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:

1. $0.28$
2. $0.02$
3. $0.3$
4. $0.5$

Q.

Two parallel forces $\mathrm{P}$ and $3\mathrm{P}$ act on a rigid body at points A and B respectively. If the forces are interchanged in position, the resultant will be displaced through a distance of

1. $\left(\frac{1}{2}\right)AB$

2. $\left(\frac{1}{3}\right)AB$

3. $\left(\frac{1}{4}\right)AB$

4. $\left(\frac{3}{4}\right)AB$

Q. A horizontal heavy uniform bar of weight 'W' is supported at its ends by two men. At the instant, one of the men lets go off his end of the rod, the other feels the force on his hand changed to

1. 
2. 
3. 
4. 

Q. A triangular plate of uniform thickness and density is made to rotate about an axis perpendicular to the plane of the paper and (a) passing through $A$, (b) passing through $B$, by the application of some force $F$ at $C$ (mid-point of $AB$) as shown in the figure. In which case, the angular acceleration is more?

1. In case (a)
2. In case (b)
3. Same in both cases
4. Cannot be determined

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. 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. What is horizontal motion?

Q. A uniform meter rule balances horizontally on a knife-edge placed at the $60cm$ mark when a weight of $1g$ is suspended from one end. What is the weight of the rule?

Q. A constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4A_0$ in $4\text{s}$. The magnitude of this torque is

1. $\frac{3A_0}{4}$
2. $4A_0$
3. $A_0$
4. $12A_0$

Q. Two small kids weighing 10kg and 15kg are trying to balance a seesaw of total length 5m with the fulcrum at the centre. If one of the kids is sitting at an end, the other should sit at

1. 1.67 m from the centre
2. 2.50 m from the centre
3. 2 m from the centre
4. 1 m from the centre

Q. A uniform meter rule balances horizontally on a knife edge placed at the $58$ cm mark when a weight of $20$ gf is suspended from one end.

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

Q. A uniform wooden stick of mass $1.6kg$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h(<l)$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of ${30}^{\circ }$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio of $h/l$ and the frictional force $f$ at the bottom of the stick are respectively
(take, $g=10m{s}^{-2}$)

1. $\frac{h}{l}=\frac{\sqrt{3}}{16},f=\frac{16\sqrt{3}}{3}N$
2. $\frac{h}{l}=\frac{3}{16},f=\frac{16\sqrt{3}}{3}N$
3. $\frac{h}{l}=\frac{3\sqrt{3}}{16},f=\frac{8\sqrt{3}}{3}N$
4. $\frac{h}{l}=\frac{3\sqrt{3}}{16},f=\frac{16\sqrt{3}}{3}N$

Q. A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of $\theta ,\text{where}\theta$ is the angle by which it has rotated, is given as $k{\theta }^2$. If its moment of inertia is $I,$ then the angular acceleration of the disc is

1. $\frac{k}{2I}\theta$
2. $\frac{2k}{I}\theta$
3. $\frac{k}{I}\theta$
4. $\frac{k}{4I}\theta$

Q. The net torque created by a force couple is

1. Always non zero
2. Always zero
3. Depends on the distance between two vectors
4. Cannot say

Q. Find the angular frequency of a mass attached to a spring, kept on a horizontal frictionless surface.

Q. A uniform thin flat isolated disc is floating in space. It has radius $R$ and mass $m$. A force $F$ is applied to it at a distance $d=\frac{r}{2}$ from the centre in the y-direction. Treat this problem as two-dimensional. Just after the force is applied :

1. acceleration of the centre of the disc is $\frac{F}{m}$.
2. angular acceleration of the disk is $\frac{F}{mR}$.
3. point which is instantaneously unaccelerated is the rightmost point.
4. acceleration of leftmost point on the disc is zero.

Q. A couple can never be replaced by a single force.

1. True
2. False

Q.

any project based on newtons third law of motion

Q. $M{L}^2{T}^{-2}$ is the dimensional formula for

1. moment of inertia
2. pressure
3. elasticity
4. couple acting on a body

Q. A square gate of size $1m\times 1m$ is hinged at its midpoint. A fluid of density $\rho$ fills the space to the left of the gate. The force $F$ required to hold the gate stationary is:

1. $\frac{\rho g}{3}$
2. $\frac{\rho g}{2}$
3. $\frac{\rho g}{6}$
4. $\frac{\rho g}{8}$

Q. A regular hexagonal uniform block of mass $m=4\sqrt{3}\text{kg}$ rests on a rough horizontal surface with coefficient of friction $\mu$ as shown in figure. A constant horizontal force is applied on the block as shown. If the friction is sufficient to prevent slipping before toppling, then the minimum force is $F$ (in $\text{N}$) that is required to topple the block about its corner $\text{A}$. Find the value of $\frac{F}{10}$
(Take $g=10{\text{m/s}}^2$)

Q. A horizontal heavy uniform bar of weight 'W' is supported at its ends by two men. At the instant, one of the men lets go off his end of the rod, the other feels the force on his hand changed to

1. $W$
2. $\frac{W}{2}$
3. $\frac{3W}{4}$
4. $\frac{W}{4}$