Intro to Torque

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

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

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

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

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

Q. The area of the parallelogram when adjacent sides are given by the vectors $\overrightarrow{A}$ = $\hat{i}+2\hat{j}+3\hat{k}$ and $\overrightarrow{B}$ = $2\hat{i}-3\hat{j}+\hat{k}$ is.

1. $\sqrt[4]{4195}$sq unit
2. \N
3. 195 sq unit
4. $\sqrt{195}$sq unit

Q. A force of $(2\hat{i}-4\hat{j}+2\hat{k})$N acts at a point $(3\hat{i}+2\hat{j}-4\hat{k})$ metre from the origin. The magnitude of torque is

1. Zero
2. 24.4 N-m
3. 0.244 N-m
4. 2.444 N-m

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. ${\omega }_A<{\omega }_B$
4. The relation depends on the actual magnitude of the torques.

Q. The the system in the figure is in equilibrium. The value of PR in terms of RQ is equal to

1. $\frac{1}{4}RQ$
2. $\frac{3}{8}RQ$
3. $\frac{3}{5}RQ$
4. $\frac{2}{5}RQ$

Q.

A particle having mass $m$ is projected with a velocity $v_0$ from a point $P$ on a horizontal ground making an angle $\theta$ with horizontal. Find out the torque about the point of projection acting on the particle when it is at its maximum height?

1. $\frac{m{v}_0^{2}sin2\theta }{4}$

2. $\frac{m{v}_0^{2}sin2\theta }{2}$

3. $\frac{m{v}_0^{2}si{n}^2\theta }{2}$

4. $\frac{2m{v}_0^{2}sin2\theta }{2}$

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

Q. A thin uniform solid wheel is initially rotating with an angular velocity $50\text{rad/s}$. The mass of the wheel is given to be $4\text{kg}$ and the radius of the wheel is $1\text{m}$. If the wheel comes to rest in $10\text{s}$, find the magnitude of the average retarding torque acting on the wheel (in $\text{N-m}$)
(Assume uniform angular retardation)

Q. If $\overrightarrow{F}$ be a force acting on a particle having the position vector $\overrightarrow{r}$ and $\overrightarrow{\tau }$ be the torque of this force about the origin, then

1. $\overrightarrow{\tau }.\overrightarrow{F}=0$ and $\overrightarrow{r}.\overrightarrow{\tau }=0$
2. $\overrightarrow{\tau }.\overrightarrow{F}=0$ and $\overrightarrow{F}.\overrightarrow{\tau }\ne 0$
3. $\overrightarrow{r}.\overrightarrow{\tau }\ne 0$ and $\overrightarrow{F}.\overrightarrow{\tau }\ne 0$
4. $\overrightarrow{r}.\overrightarrow{\tau }\ne 0$ and $\overrightarrow{F}.\overrightarrow{\tau }=0$

Q. The area of the parallelogram when adjacent sides are given by the vectors $\overrightarrow{A}$ = $\hat{i}+2\hat{j}+3\hat{k}$ and $\overrightarrow{B}$ = $2\hat{i}-3\hat{j}+\hat{k}$ is.

1. $\sqrt[4]{4195}$sq unit
2. \N
3. 195 sq unit
4. $\sqrt{195}$sq unit

Q. A square plate lies in an X-Y plane such that its centre is at the origin and can rotate about Z-Axis. A force is applied on it such that the line of force intersects Z-Axis, then.

1. the plate rotates clockwise
2. the plate rotates anticlockwise
3. there is no turning effect

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

Q. A ball is rotating in circle of radius $r$ with constant speed $u\text{m/s}$ as shown in figure. When ball is at point $a$, find the magnitude of torque acting on ball about point $b$.

1. $mu\text{N-m}$
2. $m{u}^2\text{N-m}$
3. $\frac{m}{u^2}\text{N-m}$
4. $\frac{m}{u}\text{N-m}$

Q. A ball is rotating in circle of radius $r$ with constant speed $u\text{m/s}$ as shown in figure. When ball is at point $a$, find the magnitude of torque acting on ball about point $b$.

1. $mu\text{N-m}$
2. $m{u}^2\text{N-m}$
3. $\frac{m}{u^2}\text{N-m}$
4. $\frac{m}{u}\text{N-m}$

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. ${\omega }_A<{\omega }_B$
4. The relation depends on the actual magnitude of the torques.

Q. The force on a nail which is fixed on the edge of a non-uniformly rotating disc is

1. Vertical
2. Horizontal and skew with the axis
3. Horizontal and intersecting the axis
4. None of these