Physics Question from JEE Main 2024 · 6 April, Shift 1

A $1 \, \text{kg}$ mass is suspended from the ceiling by a rope of length $4 \, \text{m}$. A horizontal force $F$ is applied at the midpoint of the rope so that the rope makes an angle of $45^\circ$ with respect to the vertical axis as shown in the figure. The magnitude of $F$ is:

The figure shows: the rope hangs from a hatched ceiling. Its upper half runs from the ceiling attachment point down and to the left to the midpoint of the rope, making $\theta = 45^\circ$ with the vertical, and the tension in this upper half is labelled $T_1$. At the midpoint the horizontal force $\vec{F}$ is applied, pointing to the left. The lower half of the rope hangs vertically from the midpoint down to the $1 \, \text{kg}$ block, and the tension in it is labelled $T_2$.