A uniform rope of length $L$ and mass $M$ is placed on a smooth fixed wedge as shown. Both ends of rope are at same horizontal level. The rope is initially released from rest, then the magnitude of initial acceleration of rope is

 

Block $B$ moves to the right with a constant velocity $v_0$. The velocity of block $A$ relative to $B$ is

System is shown in the figure and man is pulling the rope from both sides with constant speed $u$. Then the speed of the block will be ($M$ moves vertical)

In the figure shown, find out the value of $\mathrm{\theta }$ at this instant [assume string to be tight]

A hinged construction consists of three rhombus with the ratio of sides $(5:3:2)$. Vertex $A_3$ moves in the horizontal direction with velocity $V$. Velocity of $A_2$ will be

A balloon of gross weight $w$ Newton is falling vertically downward with a constant acceleration $a(<g)$. The magnitude of the air resistance is (Neglecting buoyant force)

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. Other end of the string is pulled with constant acceleration $a$ (relative to car) vertically. The tension in the string is equal to (assume $\theta$ remains constant)

Reading shown in two spring balances $S_1$ and $S_2$ is $90 \mathrm{kg}$ and $30 \mathrm{kg}$, respectively, when lift is accelerating upwards with acceleration $10 \mathrm{m} {\mathrm{s}}^{-2}$. The mass is stationary with respect to lift. Then the mass of the block will be:

In the figure a block $A$ of mass $m$ is attached at one end of a light spring and the other end of the spring is connected to another block $B$ of mass $2m$ through a light string. $A$ is held and $B$ is in static equilibrium. Now $A$ is released. The acceleration of $A$ just after that instant is $a$. In the next case, $B$ is held and $A$ is in static equilibrium. Now when $B$ is released, its acceleration immediately after the release is $b$. The value of $\frac{a}{b}$ is  (Pulley, string and the spring are massless)