In the figure shown, a balloon is pressed against a wall. It is in equilibrium and maximum compressed state.

 

$\overrightarrow{F_1}=$force of the balloon on the hand of the man, $\overrightarrow{F_2}=$force of the balloon on the wall, $\overrightarrow{F_3}=$ Friction and $\overrightarrow{F_4}=$weight of the balloon.

Which of the following statements are correct?

Consider a cart being pulled by a horse with a constant velocity. The horse exerts a force on the cart. (The subscript indicates the force on the cart due to the horse). The first subscript denotes the body on which force acts and the second due to which it acts.

Choose the correct statement(s).

Weight $W$ is supported by two strings, inclined at $60°$ and $30°$ to the vertical. The tensions in the strings are $T_1$ and $T_2$, as shown in the figure. If these tensions are to be determined in terms of $W$, using a triangle of forces, which of these triangles should you draw? (Block is in equilibrium.)

A uniform sphere of weight $w$ and radius $3\mathrm{ }\mathrm{m}$ is being held by a string of length $2\mathrm{ }\mathrm{m}$, attached to a frictionless wall, as shown in the figure. The tension in the string will be:

Two weights $W_1$ and $W_2$ in equilibrium and at rest are suspended, as shown in the figure. Then the ratio $\frac{W_1}{W_2}$ is

Four identical metal butterflies are hanging from a light string of length $5l$ at equally placed points, as shown in the figure. The ends of the string are attached to a horizontal fixed support. The middle section of the string is horizontal. The relation between angles ${\mathrm{\theta }}_1$ and ${\mathrm{\theta }}_2$ is given by

Two smooth spheres, each of radius $5\mathrm{ }\mathrm{cm}$ and weight $W$, rest one over the other, inside a fixed smooth cylinder of radius $8\mathrm{ }\mathrm{cm}$. The reactions between the spheres and the vertical side of the cylinder are

A $50 \mathrm{kg}$ person stands on a $25\mathrm{ }\mathrm{kg}$ platform. He pulls on the rope which is attached to the platform via the frictionless pulleys, as shown in the figure. The platform moves upward at a steady rate if the force with which the person pulls the rope is