$A$ rough vertical board has an acceleration $a$ so that a $2 \ kg$ block pressing against it does not fall. The coefficient of friction between the block and the board should be

$A$ girl drops an apple from the window of a train which is moving on a straight track with speed increasing at a constant rate. The trajectory of the falling apple as seen by the girl is

$A$ mass $M$ is placed on a smooth wedge of angle $\theta$ resting on a frictionless surface. To keep the mass $M$ at rest relative to the wedge,the wedge must be given a horizontal acceleration $a$ equal to:

$A$ container of mass $m$ is pulled by a constant force $F$. Inside the container,a second block of the same mass $m$ is placed,connected to the wall by a massless spring of constant $k$. Initially,the spring is at its natural length. Find the velocity of the container at the instant the compression in the spring is maximum for the first time.

$A$ block of mass $m$ is kept in an elevator which starts moving downward with an acceleration $a$ as shown in the figure. The block is observed by two observers $A$ and $B$ for a time interval $t_0$. The observer $B$ is on the ground (inertial frame). What is the work done by the pseudo force on the block as observed by observer $B$?

$A$ wedge $Y$ with mass of $10 \text{ kg}$ has all frictionless surfaces, and the inclined surface makes an angle of $37^{\circ}$ with the horizontal. $A$ block $X$ with mass $2 \text{ kg}$ is placed at the highest point of the wedge as shown in the figure and is at rest. At $t=0$, the wedge $Y$ is pulled toward the right with a constant force $f$ of $24 \text{ N}$. Taking the block $X$ at rest at $t=0$, the time taken by it to slide down $8.8 \text{ m}$ on the slope, while $Y$ is in motion, is . . . . . . s. (Take $\tan(37^{\circ}) = 3/4$ and $g = 10 \text{ m/s}^2$)