A box of mass $m$ is in equilibrium under the application of three forces as shown below. If the magnitude of $\mathbf{F}_1$ is 10 N , what is the magnitude of $\mathbf{F}_3$ ?

A block rests on a fixed wedge inclined at an angle $\theta$. The coefficient of friction between the block and plane is $\mu$. The maximum value of $\theta$ for the block to remain motionless on the

wedge is

A block of mass 4 kg at rest on a rough inclined plane making an angle of $\theta$ with the horizontal. The coefficient of static friction between the block and plane is 0.5 and the frictional force on the block is 14.14 N , find the value of $\theta$ ?

An infinite number of masses are placed on a frictionless table and they are connected via massless strings. Their masses follow the sequence, $m, \frac{m}{2}, \frac{m}{6}, \ldots \ldots \ldots . . \frac{m}{n!}, \ldots \ldots$. and they are further connected to a mass $m$ that hangs over a massless pulley. The acceleration of the hanging mass is