A block is kept on a frictionless inclined surface with angle of inclination $\alpha .$ The incline is given an acceleration $a$ to keep the block stationary. Then,$a$ is equal to
 

With what minimum acceleration mass $M$ must be moved on frictionless surface so that $m$ remains stick to it as shown? The coefficient of friction between $M \& m$ is $\mu .$

In the shown figure, the trolley move with constant acceleration $a$ and the string connecting the masses $m_1$ and $m_2.$

Make constant angles ${\theta }_1$ and ${\theta }_2.$ If$m_1=m_2=m,$ then

In the arrangement shown, system consisting of a wedge (slipping down the incline) and block $A.$ The direction of pseudo force acting on $A$ in frame of wedge is

The normal force acting on block in the situation shown is $N.$ If all the surfaces are smooth, then the value of $N$ is

In the arrangement shown, all surfaces are frictionless and pulley and string are ideal. The maximum value of $F$ so that the blocks remain at rest with respect to wedge is

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A ball of mass $\frac{1}{2} \mathrm{kg}$ is moved in a vertical circle. When ball is at $P,$ then calculate its tangential acceleration. [take, $a=10 \mathrm{m} {\mathrm{s}}^{-2}$ ]