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).

In the system shown in the figure $m_1>m_2$. System is held at rest by thread $BC$. Just after the thread $BC$ is burnt:

A light string is wrapped round a cylindrical log of wood which is placed on a horizontal surface with its axis vertical and it is pulled with a constant force $F$ as shown in the figure. (Friction is absent everywhere)

Two blocks of mass $M$ and $m$ are used to compress two different massless springs, as shown. The left spring is compressed by, $3 \mathrm{cm}$ while the right spring is compressed by an unknown amount. The system is at rest and all surfaces are fixed and smooth. Which of the following statements are true?

In the figure shown, all the surfaces are smooth. All the blocks $A$, $B$ and $C$ are movable, $x$-axis is horizontal and $y$-axis is vertical, as shown. Just after the system is released from the position as shown,

A block $A (5 \mathrm{kg})$ rests over another block $B\mathit{ }(3 \mathrm{kg})$ placed over a smooth horizontal surface. There is friction between $A$ and $B$. A horizontal force $F_1$, gradually increasing from zero to a maximum, is applied to $A$, so that the blocks move together without relative motion. Instead of this, another horizontal force $F_2$, gradually increasing from zero to a maximum, is applied to $B$, so that the blocks move together without relative motion. Then,

${\mathrm{M}}_{\mathrm{A}}=3 \mathrm{kg}, {\mathrm{M}}_{\mathrm{B}}=4 \mathrm{kg}$ and ${\mathrm{M}}_{\mathrm{C}}=8 \mathrm{kg}$. The coefficient of friction between any two surface is $0.25$. The pulley is frictionless and the string is massless. $A$ is connected to a wall by a massless rigid rod.