The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium,the angle $\theta$ should be ........ $^o$.

Block $A$ of mass $m$ and block $B$ of mass $M$ are connected by a massless spring over a pulley on a rough plane with coefficient of friction $\mu$. $A$ force $F$ is applied on block $A$ to the left. Find the minimum value of $M$ to move the block $A$ towards the right.

$A$ ball is dropped on the floor from a height of $20 \ m$. It rebounds to a height of $5 \ m$. The ball remains in contact with the floor for $1 \ s$. The average acceleration during contact is (acceleration due to gravity $g = 10 \ m/s^2$): (in $m/s^2$)

Two blocks of mass $2 \ kg$ and $1 \ kg$ are connected by an ideal spring on a rough surface. The spring is unstretched. The spring constant is $8 \ N/m$. The coefficient of friction is $\mu = 0.8$. Now,the $2 \ kg$ block is imparted a velocity $u$ towards the $1 \ kg$ block. Find the maximum value of velocity $u$ of the $2 \ kg$ block such that the $1 \ kg$ block never moves.

$A$ boy of mass $4 \, kg$ is standing on a piece of wood having mass $5 \, kg$. If the coefficient of friction between the wood and the floor is $0.5$,the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is ...... $N$. (Round off to the Nearest Integer) [Take $g = 10 \, m s^{-2}$]

The curve between net force and time is shown. Initially,the particle is at rest. Which of the following best represents the resulting velocity-time graph of the particle?