Adjoining figure shows a force of $40\, N$ acting at $30^o$ to the horizontal on a body of mass $5 \,kg$ resting on a smooth horizontal surface. Assuming that the acceleration of free-fall is $10\, ms^{-2}$, which of the following statements is (are) correct?

$[1]$ The horizontal force acting on the body is $20\, N$

$[2]$ The weight of the $5\, kg$ mass acts vertically downwards

$[3]$ The net vertical force acting on the body is $30\, N$

Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface., the acceleration of mass $m$ is

Three blocks $A$, $B$ and $C$ are pulled on a horizontal smooth surface by a force of $80 \mathrm{~N}$ as shown in figure

The tensions $T_1$ and $T_2$ in the string are respectively

Calculate $T_1$ and $T_2$

A rod of length $L$ and mass $M$ is acted on by two unequal forces $F_1$ and $F_2 (< F_1 )$ as shown in the following figure.The tension in the rod at a distance $y$ from the end $A$ is given by

A pebble of mass $0.05\; kg$ is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble,

$(a)$ during its upward motion,

$(b)$ during its downward motion,

$(c)$ at the highest point where it is momentarily at rest.

Do your answers change if the pebble was thrown at an angle of $45^o$ with the horizontal direction? Ignore air resistance.