Torque

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:

In a movable pulley (single moving pulley), the load is $100 \mathrm{N}$. Find the effort in newtons, if the efficiency is $100$ percentage.

In a movable pulley (single moving pulley), the load is $100 \mathrm{N}$. Find the mechanical advantage, if the efficiency is $100$ percentage.

A particle of mass M tied to a string of length L is rotating along a circular path with constant speed $\mathrm{\vartheta }$. The torque on the particle is

Which lever has mechanical advantage always greater than one?

The principle of a lever is the principle of law of:

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

A slender uniform rod of mass M and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is:

In a physical balance working on the principle of moments, when $5mg$ weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

A force of $40 \mathrm{N}$ acts on a point $B$ at the end of an L-shaped object as shown in the figure. The angle $\theta$ that will produce maximum moment of the force about point $A$ is given by:

A solid cylinder of mass $50\mathrm{ }\mathrm{k}\mathrm{g}$ and radius $0.5\mathrm{ }\mathrm{m}$ is free to rotate about 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 $2$ revolutions $s^{-2}$

A uniform rod $AB$ of mass $m$ and length $l$is at rest on a smooth horizontal surface. An impulse $J$is applied to the end$B$ perpendicular to the rod in a horizontal direction. Speed of particle $P$at a distance $\frac{l}{6}$ from the centre towards $A$ of the rod after time, $t=\frac{\mathrm{\pi }ml}{12J}$ is

A force $\overrightarrow{F}=4\hat{\mathrm{i}}-10\hat{\mathrm{j}}$ acts on a body at a point having position vector $\overrightarrow{r}=-5\hat{\mathrm{i}}-3\hat{\mathrm{j}}$ relative to origin of coordinates on the axis of rotation. If the torque acting on the body about origin is $a\hat{\mathrm{k}}$, then find the value of $a$ (in SI units). [Given, $\overrightarrow{F}$ and $\overrightarrow{r}$ are in SI units]

Which relation is not correct of the following?

What are the rotational equivalents for the physical quantity force?

Class III lever acts as a _____ multiplier.

(Choose from the following: force / speed)

The handle of a nut-cracker is $16 \mathrm{cm}$ long and a nut is placed $2 \mathrm{cm}$ from its hinge. If a force of $4 \mathrm{kgf}$ is applied at the end of handle to crack it, what weight (in $\mathrm{kgf}$), if simply, placed on the nut will crack it?

A resistance of $2000 \mathrm{N}$ is overcome by a machine of velocity ratio $5$ and efficiency $75\%$. If the effort required to overcome resistance is $x$ $\mathrm{N}$, then the value of $x$ is?  (Give your answer up to two decimal places)

A fire tong has its arms $20 \mathrm{cm}$ long. It is used to lift a coal of weight $1.5 \mathrm{kgf}$ by applying an effort at a distance $15 \mathrm{cm}$ from fulcrum. The effort needed is:

A worker is pushing a box weighing $1500 \mathrm{N}$ up a ramp $6 \mathrm{m}$ long onto a platform $1.5 \mathrm{m}$ above ground. What is the mechanical advantage?