$A$ constant force $F$ is applied in the horizontal direction as shown. If the contact force between $M$ and $m$ is $N$ and the contact force between $m$ and $M'$ is $N'$,then:

$A$ ball of mass $2 \ kg$ is moving in $xy$-plane with a potential energy given as $U=(12x + 16y) \ J$, where $x$ and $y$ are in metres. Assume the initial position of the ball at $t=0$ is at the origin $(0,0)$ and it is moving with a velocity of $(15 \hat{i} + 20 \hat{j}) \ m/s$. Identify the correct statement.

$A$ block of mass $m$ is placed on a smooth horizontal surface. $A$ force making an angle $\theta$ with the horizontal starts acting on the block. The magnitude of the force is constant but its direction with the horizontal changes as $\theta = a + bs$,where $a$ and $b$ are constants and $s$ is the distance covered by the block. If $|F| = 2mb$,find the velocity of the block as a function of the angle $\theta$.

The driver of a car travelling at velocity $v$ suddenly sees a broad wall in front of him at a distance $d$. He should

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:

Masses of $10\, kg$ and $20\, kg$ are connected by a massless spring as shown in the figure. $A$ force of $200\, N$ acts on the $20\, kg$ mass. At the instant shown,the $10\, kg$ mass has an acceleration of $12\, m/s^2$. What is the acceleration of the $20\, kg$ mass in $m/s^2$?