In the figure shown $C$ is a fixed wedge. A block $B$ is kept on the inclined surface of the wedge $C$. Another block $A$ is inserted in a slot in the block $B$ as shown in figure. A light inextensible string passes over a light pulley which is fixed to the block $B$ through a light rod. One end of the string is fixed and other end of the string is fixed to $A$. $S$ is a fixed support on the wedge. All the surfaces are smooth. Masses of $A$ and $B$ are same. Then the magnitude of acceleration of $A$ is $\frac{\sqrt{x}}{3} \mathrm{m} {\mathrm{s}}^{-2}.$ Then $x$ is $(\sin 37°=\frac{3}{5})$

 

In the arrangement shown in the fig, the block of mass $m=2 \mathrm{kg}$ lies on the wedge of mass $M=8 \mathrm{kg}$. The initial acceleration of the wedge if the surfaces are smooth and pulley & strings are massless is $\frac{30\sqrt{3}}{x}\mathrm{m} {\mathrm{s}}^{-2}$ then $x$ is 

Two particles $A$ and $B$ of masses $3 \mathrm{kg}$ and $2 \mathrm{kg}$ are connected by a light inextensible string. The particles are in contact with the smooth faces of a wedge $DCE$ of mass $10 \mathrm{kg}$ resting on a smooth horizontal plane. When the system is moving freely, find the acceleration of the wedge (in $\mathrm{cm} {\mathrm{s}}^{-2}$). Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

(Approximate the answer to one decimal place)

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 particle is resting on a smooth horizontal floor. At $t=0$, a horizontal force starts acting on it. Magnitude of the force increases with time according to law $F=\alpha t$, where $\alpha$ is a constant. For the figure shown which of the following statements is/are correct?

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 $A$ and $B$ of mass $10 \mathrm{kg}$ and $40 \mathrm{kg}$ are connected by an ideal string as shown in the figure. Neglect the masses of the pulleys and effect of friction. $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

Two blocks of masses $10 \mathrm{kg}$ and $20 \mathrm{kg}$ are connected by a light spring as shown. A force of $200 \mathrm{N}$ acts on the $20 \mathrm{kg}$ mass as shown. At a certain instant the acceleration of $10 \mathrm{kg}$ mass is $12 {\mathrm{ms}}^{–2}$ towards right direction.