A wedge is moving with an acceleration, $a=4 \mathrm{m} {\mathrm{s}}^{-2}$ vertically up as shown in figure. What is acceleration of a block of mass $1 \mathrm{kg}$ w.r.t. wedge and normal reaction by wedge on block, respectively. All surfaces are smooth and $\theta =30°$. Choose the correct pair $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$.

A container of liquid is released from the rest, on a smooth inclined plane as shown in the figure. Length of at the inclined plane is sufficient, and assume liquid finally equilibrium. Finally, the liquid surface makes an angle horizontal.......

A triangular block of mass $M$ rests on a smooth surface as shown in figure. A cubical block of mass $m$ rests on the inclined surface. If all surfaces are frictionless, the force that must be applied to $M$ so as to keep $m$ stationary relative to $M$ is,

According to figure, the reading of the spring balance will be $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$,

A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration $a$ directed horizontally as shown in figure. The other end of the string is pulled with constant acceleration $a$ (relative to car) vertically. The tension in the string is equal to,

The ratio of acceleration of $A$ and $B$ is,

A perfect smooth sphere $A$ of mass $2 \mathrm{kg}$ is in contact with a rectangular block $B$ of mass $4 \mathrm{kg}$ and vertical wall as shown in the figure. All surfaces are smooth. Find normal reaction by vertical wall on sphere $A$.

A flexible chain of weight $W$ hangs between two fixed points $A$ and $B$ at the same level. The inclination of the chain with the horizontal at the two points of support is $\theta .$ What is the tension of the chain at the two segments

A cylinder rests in a supporting carriage as shown. The side $AB$ of carriage makes an angle $30°$ with the horizontal and side $BC$ is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with a horizontal acceleration $a$. The magnitude of normal reactions exerted by sides $AB$ and $BC$ of carriage on the cylinder are $N_{\mathrm{AB}}$ and $N_{\mathrm{BC}}$, respectively. Neglect friction everywhere. Then, as the magnitude of acceleration $a$ of the carriage is increased, pick up the correct statement.