A rod of mass $1\ kg$ , length $1\ m$ is suspended horizontally with the help of two ideal strings as shown in figure. First a mass is suspended to the left most end keeping rod horizontal, than a second mass is suspended to the right most end again keeping horizontal orientation. The maximum total mass that can be suspended in that way keeping horizontal orientation of rod ……. $kg.$

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.

A disc of radius $20\, cm$ and mass half $kg$ is rolling on an inclined plane. Find out friction force so that disc performs pure rolling.

$A$ sphere is placed rotating with its centre initially at rest ina corner as shown in figure $(a)$ & $(b)$. 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 $(a)$ & $(b)$.

A solid cylinder of mass $m$ is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is:

[The coefficient of static friction, $\mu_{ s },$ is $\left.0.4\right]$