End $A$ of the bar $AB$ in figure rests on a frictionless horizontal surface and end $B$ is hinged. $A$ horizontal force $\overrightarrow{F}$ of magnitude $120 \mathrm{N}$ is exerted on end $A.$ You can ignore the weight of the bar. What is the net force exerted by the bar on the hinge at $B?$

Find minimum height of obstacle so that the sphere can stay in equilibrium

A sphere is placed rotating along its centre and initially at rest in a comer as shown in figure $\left(A\right) \text{\&} ( B)$. The coefficient of friction between all surfaces and the sphere is $\frac{1}{3}$. Find the ratio of the frictional force $\frac{f_A}{f_B}$ by ground in situations $\left(A\right) \text{\&} \left(B\right)$ is:

Two painters are working from a wooden board $5 \mathrm{m}$ long suspended from the top of a building by two ropes attached to the ends of the plank. Either rope can withstand a maximum tension of $1040 \mathrm{N}.$ Painter $A$ of mass $80 \mathrm{kg}$ is working at a distance of $1 \mathrm{m}$ from one end. Painter $B$ of mass $60 \mathrm{kg}$ is working at a distance of $x \mathrm{m}$ from the centre of mass of the board on the other side. Take mass of the board as $20 \mathrm{kg}$ and $g=10 \mathrm{m}{\mathrm{s}}^{-2}.$ The range of $x$ so that both the painters can work safely is

In figure, a massive rod $AB$ is held in horizontal position by two massless strings. If the string at $B$ breaks and if the horizontal acceleration of centre of mass, vertical acceleration and angular acceleration of rod about the centre of mass are $a_x, a_y$ and $\alpha ,$ respectively, then

A uniform cylinder of mass $M$ lies on a fixed plane inclined at an angle $\theta$ with horizontal. A light string is tied to the cylinder at the right most point, and a mass $m$ hangs from the string, as shown. Assume that the coefficient of friction between the cylinder and the incline plane is sufficiently large to prevent slipping. For the cylinder to remain static, the value of $m$ is

A cylinder of height $H$ and diameter $H/4$ is kept on a frictional turntable as shown in figure. The axis of the cylinder is perpendicular to the surface of the table and the distance of axis of the cylinder is $2H$ from the centre of the table. The angular speed of the turntable at which the cylinder will start toppling (assume that friction is sufficient to prevent slipping) is

A disc of mass $m$ and radius $R$ placed on a smooth horizontal table as shown in figure. A light ideal string passes through the disc such that the one end of the string is attached to a small body of mass $m$ and the other end is being pulled with a force $F.$ The circumference of the disc is sufficiently rough so that the string does not slip over it. Find acceleration of the small body.

Find minimum value of $l$ so that truck can avoid the dead end, without toppling the block kept on it.