Intro to Torque

Q. A solid cylinder of mass $2kg$ and radius $4cm$ is rotating about its axis at the rate of $3rpm$. The torque required to stop after $2\pi$ revolutions is

1. $2\times {10}^{-6}Nm$
2. $2\times {10}^{-3}Nm$
3. $12\times {10}^{-4}Nm$
4. $2\times {10}^{6}Nm$

Q. A rope is wound around a hollow cylinder of mass $3$ $kg$ and radius $40$ $cm$. What is the angular acceleration of the cylinder if the rope is pulled with a force of $30$ $N$?

1. $25$ $rad{s}^{-2}$
2. $20$ $rad{s}^{-2}$
3. $25$ $m{s}^{-2}$
4. $20$ $m{s}^{-2}$

Q. A solid cylinder of mass $50\text{kg}$ and radius $0.5\text{m}$ is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of $2{\text{rev/s}}^2$ is

1. $25\text{N}$
2. $157\text{N}$
3. $50\text{N}$
4. $8.5\text{N}$

Q.

Two blocks of masses 2kg and 4 kg are hanging with the help of massless string passing over an ideal pulley inside an elevator. The elevator is moving upward with an acceleration of g/2.the tension in the string connected between the two blocks will be.

Q. Moment of inertia of a uniform circular ring of mass $m$ and radius $R$ about its diameter is

1. $m{R}^2$
2. $2m{R}^2$
3. $\frac{m{R}^2}{2}$
4. $\frac{m{R}^2}{4}$

Q. An automobile moves on a road with a speed of $54\text{km/hr}$. The radius of its wheels is $0.45\text{m}$ and the moment of inertia of the wheel about its axis of rotation is $3{\text{kg-m}}^2$. If the vehicle is brought to rest in $15\text{s}$, the magnitude of average torque transmitted by its brakes to the wheel is

1. $2.86{\text{kg m}}^2{\text{s}}^{-2}$
2. $6.66{\text{kg m}}^2{\text{s}}^{-2}$
3. $8.58{\text{kg m}}^2{\text{s}}^{-2}$
4. $10.86{\text{kg m}}^2{\text{s}}^{-2}$

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

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

Q. A pulley of radius $2\text{m}$ is rotated about its axis by a force $F=(20t-5t^2)\text{N}$ (where $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10{\text{kgm}}^2$, the number of rotations made by the pulley before its direction of motion is reversed, is

1. Less than 3
2. More than 3 but less than 6
3. More than 6 but less than 9
4. More than 9

Q. A door $1.6\text{m}$ wide requires a minimum force of $1\text{N}$ to be applied at the free end to open or close it. The minimum force that is required at a point $0.4\text{m}$ away from the hinges for opening or closing the door is

1. $1.2\text{N}$
2. $2.4\text{N}$
3. $3.6\text{N}$
4. $4\text{N}$

Q. A uniform circular disc $A$ of radius $r$ is made from a metal plate of thickness $t$ and another uniform circular disc $B$ of radius $4r$ is made from the same metal plate of thickness $\frac{t}{4}$. Equal torque acts on both the discs $A$ and $B$, initially both being at rest. If at a later instant, the angular speeds of disc $A$ and $B$ are ${\omega }_A$ and ${\omega }_B$ respectively, then we have

1. ${\omega }_A={\omega }_B$
2. ${\omega }_A>{\omega }_B$
3. The relation depends on the actual magnitude of the torques.
4. ${\omega }_A<{\omega }_B$

Q. A wheel having moment of inertia $I=4{\text{kg-m}}^2$ about its natural axis is rotating at the rate of ${\omega }_o=120\text{rpm}$. Find the magnitude of constant torque which can stop the wheel in $3$ minutes.

1. $2\pi /45\text{N-m}$
2. $16\pi /3\text{N-m}$
3. $160\text{N-m}$
4. $4\pi /45\text{N-m}$

Q.

State the two factors on which moment of a force depends:

Q. The width of a door is $40\text{cm}$. If it is released by exerting a force of $2\text{N}$ perpendicularly at its edge (away from the hinges). Compute the magnitude of torque produced which causes the door to open.

1. $10\text{Nm}$
2. $6\text{Nm}$
3. $0\text{Nm}$
4. $8\text{Nm}$

Q. If the de Broglie wavelength of a particle of mass M is 100 times its velocity then its value in terms of its mass and Plancks Constant is

Q.

Calculate the total torque acting on the body shown in figure about the point $O$.

1. 0.54 N - m

2. 54 N - m

3. 45 N - m

4. 0.45 N - m

Q. A particle is projected with a velocity of 30 m/s, at an angle of ${\theta }_0=ta{n}^{-1}\left(3/4\right)$. After 1 second, the particle is moving at an angle $\theta$ to the horizontal, where tan $\theta$ is given by $(g=10m{s}^{-2})$

1. 1
2. 2
3. 1/2
4. 1/3

Q.

A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after $2\pi$ revolutions is

1. $2\times {10}^{-6}$ Nm
2. $2\times {10}^{-3}$ Nm
3. $12\times {10}^{-4}$ Nm
4. $2\times {10}^6$ Nm

Q. A ball of mass $m=2\text{kg}$ is projected at an angle $\theta ={45}^{\circ }$ with initial velocity of $u=10\text{m/s}$ as shown in figure. Find the torque acting on the particle due to gravity about origin at it's maximum height.
(Take $g=10m/s^2$)

1. $100\hat{k}$
2. $10\hat{k}$
3. $-100\hat{k}$
4. $-10\hat{k}$

Q. A uniform ring of radius $R$, is fitted with a massless rod $AB$ along its diameter. An ideal horizontal string (whose one end is attached with the rod at a height $r$) passes over a smooth pulley and other end of the string is attached with a block of mass double the mass of ring as shown. The co-efficient of friction between the ring and the surface is $\mu$. When the system is released from rest, the ring moves such that rod $AB$ remains vertical . The value of $r$ is

1. $R(1-\frac{3\mu }{2(1+\mu )})$
2. $R(1-\frac{\mu }{2(1+\mu )})$
3. $R(1-\frac{3\mu }{(1+\mu )})$
4. $R(2-\frac{3\mu }{2(1+\mu )})$

Q. A door is hinged at one end and free to rotate about a vertical axis as shown in figure. Does its weight cause any torque about vertical axis?

1. Yes
2. No
3. None of these
4. Cannot be determined

Q. For a force $F$ acting on rigid body,
Statement $1:$ Component of torque about any point lying on the axis, along the axis is defined as torque about that axis.
Statement $2:$ Torque about an axis is same as torque about any point lying on that axis.

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

Q. A rope is wound around a hollow cylinder of mass $3kg$ and radius $40cm$. What is the angular acceleration of the cylinder if the rope is pulled with a force of $30N$.

1. $5m/s^2$
2. $25rad/s^2$
3. $25m/s^2$
4. $0.25rad/s^2$

Q. For a wheel rotating at a rate of $60\text{rpm}$ about an axis passing through its centre, the torque required to stop wheel's rotation in 2 minute will be (Given : MOI of wheel about its axis is $4{\text{kg m}}^2)$

1. $\frac{\pi }{30}\text{N.m}$
2. $\frac{\pi }{60}\text{N.m}$
3. $\frac{\pi }{15}\text{N.m}$
4. $\frac{2\pi }{15}\text{N.m}$

Q. $ABCD$ is a square, $O$ is the center of the square. $\overrightarrow{F_1}$, $\overrightarrow{F_2}$, $\overrightarrow{F_3}$ and $\overrightarrow{F_4}$ represent four forces acting along sides $AB,BC,CA$ and $AD$ respectively. If torque about $O$ is zero then $|\overrightarrow{F_2}|$ is

1. $F_1-F_3+F_4$
2. $F_1+F_3+F_4$
3. $F_1+F_3-F_4$
4. $F_1-F_3-F_4$

Q. Find the total torque acting on the body shown in the figure about the point $O$

1. $2Fr\text{N-m}$
2. $Fr\text{N-m}$
3. $0\text{N-m}$
4. $\frac{Fr}{2}\text{N-m}$

Q. Moment of force $\left(\overrightarrow{F}\right)$ about an axis $\left(\overrightarrow{AB}\right)$ is zero when

1. $\overrightarrow{F}||\overrightarrow{AB}$
2. $\overrightarrow{F}$ intersects $\overrightarrow{AB}$
3. $\overrightarrow{F}\perp \overrightarrow{AB}$
4. Both (a) and (b)

Q. A solid cone hangs from a frictionless pivot at the origin $O$ as shown. If $\hat{i},\hat{j},\hat{k}$ are unit vectors and $a,b,$ and $c$ are positive constants, determine the torque generated about the origin by a force $F=a\hat{j}\text{N}$ applied to the rim of the cone at a point $P(-b,0,–c)$?

1. $\overrightarrow{\tau }=ab\hat{i}$
2. $\overrightarrow{\tau }=-ab\hat{k}+ac\hat{i}$
3. None of these
4. $\overrightarrow{\tau }=-ab\hat{i}$

Q. Find the torque by the force, $\overrightarrow{F}=2\hat{i}+3\hat{j}+5\hat{k}$ acting at the point $\overrightarrow{r_1}=5\hat{i}+2\hat{j}-\hat{k}$ about the point $\overrightarrow{r_2}=6\hat{i}-4\hat{j}+\hat{k}$.

1. $15\hat{i}+\hat{j}+36\hat{k}$
2. $36\hat{i}+\hat{j}-15\hat{k}$
3. $\hat{i}+36\hat{j}-15\hat{k}$
4. $36\hat{i}-15\hat{j}+\hat{k}$

Q. Two boys having masses $m_1=4\text{kg}$ and $m_2=2\text{kg}$ are seating on a seesaw of length $r=1\text{m}$ as shown in figure. Find the net torque due to weight of boys, acting about the midpoint $O$.
(Take $g=10{\text{m/s}}^2$ and anti-clock wise rotation as $+ve$)

1. $10\text{N-m}$
2. $-20\text{N-m}$
3. $-10\text{N-m}$
4. $20\text{N-m}$

Q. A ball of mass $m=2\text{kg}$ is travelling under the influence of gravity. At height $H=5\text{m}$ speed of ball is $u=10\text{m/s}$ as shown in figure. Find the torque due to gravity about $x$ axis.

1. $20\text{N-m}$
2. $10\text{N-m}$
3. $0\text{N-m}$
4. $30\text{N-m}$