$ABC$ is an equilateral triangle with $O$ as its centre. $\vec F_1, \vec F_2 $and $\vec F_3$ represent three forces acting along the sides $AB, BC$ and $AC$ respectively. If the total torque about $O$ is zero then the magnitude of $\vec F_3$ is
$({F_1} + {F_2})/2$
$2\,({F_1} + {F_2})$
$({F_1} + {F_2})$
$({F_1} - {F_2})$
$A$ uniform ladder of length $5m$ is placed against the wall as shown in the figure. If coefficient of friction $\mu$ is the same for both the walls, what is the minimum value of $\mu$ for it not to slip?
A smooth rod of length $l$ is kept inside a trolley at an angle $\theta$ as shown in the figure. What should be the acceleration a of the trolley so that the rod remains in equilibrium with respect to it?
A uniform beam of weight $W$ is attached to a vertical wall by a hinge $H$ . The beam is held horizontal by a rope as shown below. Which one of the following best shows the direction of the reaction force $R$ at the hinge ?
A car wetghs $1800\; kg$. The distance between its front and back axles is $1.8\; m$. Its centre of gravity is $1.05\; m$ behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.
Two vertical walls are separated by a distance of $2\ m$. Wall $A$ is smooth while wall $B$ is rough with a coefficient of friction $0. 5$. A uniform rod is placed between them as shown. The length of longest rod that can be placed between walls is equal to