A mass of $10 \mathrm{kg}$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the mass, the rope deviated at an angle of $45°$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (Take, $g=10 {\mathrm{ms}}^{-2}$ )

A particle of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t=0$, a force $F=kt$ acts in the same direction in which the particle is moving in time interval $T$ so that its momentum changes from $p$ to $3p$. Here $k$ is a constant. The value of $T$ is:

A vessel containing water is given a constant acceleration $a$ towards the right, along a straight horizontal path. Which of the following diagram represents the surface of the liquid?

The effective spring constant of two spring systems as shown in the figure will be: