Torque

A planet of mass $m$ is in an elliptical orbit about the sun $\left(m<<M_{\text{sun}}\right)$ with an orbital period $T$. If $A$ be the area of orbit, then its angular momentum would be

On the rotating disc $A$ of mass$M$, another disc of same dimension but of mass$\frac{ M}{4}$is placed gently with same axis. New angular velocity of system.

A particle of mass $1 \mathrm{kg}$ is moving along the line $y = x + 3$ ($x$ and$y$ are in meter) with speed $3 \mathrm{m} {\mathrm{s}}^{-1}$. The magnitude of angular momentum of the particle about origin is

A uniform wooden beam AB, $80 \mathrm{cm}$ long and weighing $200 \mathrm{gf}$, is supported on a wedge as shown in the figure. Calculate the greatest weight which can be placed on end A without causing the beam to tilt.

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

If the earth suddenly shrinks to $\frac{1}{64}\mathrm{th}$ of its original volume with its mass remaining the same, the period of rotation of earth becomes $\frac{24}{x}h$. The value of $x$ is ________

A solid sphere rolls on a horizontal plane. The ratio of angular momentum about COM to total energy is $\frac{\pi }{22}$. The angular speed of the sphere is $x \mathrm{rad} {\mathrm{s}}^{-1}$. Find the value of $x$

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 sphere is released on a smooth inclined plane from the top. When it moves down its angular momentum is:
 

Find the relation between angular momentum and torque.

A uniform rectangular box of dimensions $(40 \mathrm{cm} \times 20 \mathrm{cm})$ is kept on a horizontal smooth surface at a distance $10 \mathrm{m}$ from a wall. A constant force $F$ has to applied horizontally at the highest point as shown. The minimum time (in seconds) to reach the wall without causing the box to rotate is

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

A uniform solid cylinder of mass $1 \mathrm{kg}$ and radius $20 \mathrm{cm}$ rotates about a fixed vertical frictionless axle with an angular speed of $50\mathrm{rad} {\mathrm{s}}^{-1}$. A particle of mass $0.5 \mathrm{kg}$ now sticks on cylinder at a distance of $15 \mathrm{cm}$ from the axle. Magnitude of change in angular velocity (in $\mathrm{rad} {\mathrm{s}}^{-1}$) of the cylinder is