Moment of Force and Torque

A light rope is wound around a hollow cylinder of mass $5 \mathrm{kg}$ and radius $70 \mathrm{cm}$. The rope is pulled with a force of $52.5 \mathrm{N}$. The angular acceleration of the cylinder will be _____ $\mathrm{rad} {\mathrm{s}}^{-2}$.

A force of $-P\hat{k}$ acts on the origin of the coordinate system. The torque about the point $(2,-3)$ is $P(a\hat{i}+b\hat{j})$, The ratio of $\frac{a}{b}$ is $\frac{x}{2}$. The value of $x$ is

A wheel of mass $60 \mathrm{kg}$ and radius of gyration $0.5 \mathrm{m}$ comes to rest from a speed of $2400 \mathrm{rpm}$ in$40$second. Assuming that the retardation is uniform, the value of the retarding torque is :

A force $F$ is applied on a disk at some distance $x$ from the centre. What should be the value of $x$ such that the disk can pure roll even on smooth surface?

A square plate of side $a$ and mass $m$ is lying on a horizontal floor. A force $F$ is applied at the top. Find the maximum force that can be applied on the square plate so that the plate does not topple about $A$.

Angular speed $\omega$ versus time$t$ for a rod that rotates around one end is shown. If moment of inertia of rod about its one end is $24 \mathrm{kg} {\mathrm{m}}^2$, then torque on the rod at $t=2 \mathrm{s}$ is

 A rod $PQ$ of mass $10 \mathrm{kg}$ and length$2 \mathrm{m}$ is hinged at end $P$. The rod is kept horizontal by a massless string tied to point$Q$as shown in figure. When string is cut, the initial angular acceleration of the rod is (in $\mathrm{rad} {\mathrm{s}}^{-2}$):-

 

A uniform rod weighs $10 \mathrm{kg}$ and with a load $5 \mathrm{kg}$ attached to one end, it balances on a knife edge at $2 \mathrm{m}$ from that end. The length of rod is

Forces act as indicated on a rod $AB$ which is pivoted at $A$. Find the anticlockwise moment of each force about the pivot.

Horizontal rod of length $1 \mathrm{m}$ given below is in equilibrium. If the potential energies of objects $A$ and $B$ are equal, find the tension (in N) in string $xy$. (Rod is homogeneous and weight of it is $1 \mathrm{N}$ .

zero potential energy level

If force $\overrightarrow{F}=3\hat{\mathrm{i}}+4\hat{\mathrm{j}}-2\hat{\mathrm{k}}$ acts on a particle having position vector $2\hat{\mathrm{i}}+\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ then, the torque about the origin will be:

$ABC$ is an equilateral triangle with $O$ as its centre ${\overrightarrow{F}}_1,{\overrightarrow{F}}_2$ and ${\overrightarrow{F}}_3$. represent three forces acting along the sides $AB, BC$ and $AC$ respectively. If the total torque about $O$ is zero then the magnitude of $F_3$ is

Two like parallel forces $20 \mathrm{N}$ and $30 \mathrm{N}$ act at the ends $A$ and $B$ of a rod $1.5 \mathrm{m}$ long. The resultant of the forces will act at the point

A uniform rod of length $l$ and weight $W$ is in equilibrium with the help of hinge $A$ and string $BD$ as shown in figure. The value of tension in the string is

A disc like reel on massless thread unrolls itself while falling vertically downwards. The acceleration of its fall is

Magnitude of Torque of force $\overrightarrow{f}=\left(2\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}\right) \mathrm{N}$ acting at $\left(-5,2,1\right) \mathrm{m}$ about the origin is:

What is the difference between torque and force?

A uniform, rigid, square loop of mass ' $m$ ' side '$l$' is free to rotate about an axis in $x y$ plane passing through one corner as shown. A constant current $I$ is flowing in loop In space magnetic field $B_0\left(1+\frac{x}{l}\right)(\hat{i}+\hat{k})$ is present. Initially loop is held at rest in $xy$ plane. On releasing it's instantaneous angular acceleration will be (space is gravity free).

A uniform thin rod with mass $M$ and length $L$ is initially held at angle ${\theta }_0=53°$ with the ground as shown. A small light cup is fixed at the higher end of rod with mouth facing outward and a small light ball is put inside the cup, as shown in figure. The rod is then released from rest to hit the ground. It is assumed that the friction of the ground is large enough so that contact point of rod and ground remains same, when the rod falls. At angle $\theta$ the ball starts to move out of the cup.

A uniform rigid rod hinged at one end is released from rest in the position shown in the vertical plane. The magnitude of reaction force (in $N$ ) at hinge just after its release. Express your answer after rounding it to nearest integer. (Use: mass of rod$=0.8 \mathrm{kg}$, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)