Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is \(0.05\).
( \(g=10 \mathrm{~m} / \mathrm{s}^2\), mass of the string is negligible and no other friction exists ). 

           
1. \( 1.25 \mathrm{~m} / \mathrm{s}^2 \)
2. \( 1.50 \mathrm{~m} / \mathrm{s}^2 \)
3. \( 1.66 \mathrm{~m} / \mathrm{s}^2 \)
4. \( 1.00 \mathrm{~m} / \mathrm{s}^2\)

A body of mass \(m\) is kept on a rough horizontal surface (coefficient of friction =\(\mu)\). A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by \(\vec F\) where:
1. \(|{\vec F}| = mg+\mu mg\)
2. \(|\vec F| =\mu mg\)
3. \(|\vec F| \le mg\sqrt{1+\mu^2}\)
4. \(|\vec F| = mg\)