$A$ box '$A$' is lying on the horizontal floor of the compartment of a train running along horizontal rails from left to right. At time '$t$',it decelerates. Then the reaction $R$ by the floor on the box is given best by

The system shown in the figure is in equilibrium and at rest. The spring and string are massless. Now,the string is cut. The acceleration of mass $2m$ and $m$ just after the string is cut will be:

Explain why
$(a)$ a horse cannot pull a cart and run in empty space,
$(b)$ passengers are thrown forward from their seats when a speeding bus stops suddenly,
$(c)$ it is easier to pull a lawn mower than to push it,
$(d)$ a cricketer moves his hands backwards while holding a catch.

$A$ $500 \, kg$ horse pulls a cart of mass $1500 \, kg$ along a level road with an acceleration of $1 \, m/s^2$. If the coefficient of sliding friction is $0.2$,then the force exerted by the horse in the forward direction is ......... $N$.

$A$ spring-block system is placed on a rough horizontal floor. The block is pulled towards the right to give the spring an elongation $x_0$ such that $\frac{\mu mg}{K} < x_0 < \frac{2\mu mg}{K}$,and then released. Which of the following statements is correct?

$A$ block of mass $M$ is placed on a horizontal surface and is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. The surface under $M$ is smooth,while the vertical surface under $m$ is rough with a coefficient of friction $\mu$. The minimum value of $\mu$ for which the block $m$ remains stationary is: