$A$ 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 $g = 10 \, m s^{-2}$]

Three forces $\vec{F}_1=(2 \hat{i}+4 \hat{j}) \,N$,$\vec{F}_2=(2 \hat{j}-\hat{k}) \,N$,and $\vec{F}_3=(\hat{k}-4 \hat{i}-2 \hat{j}) \,N$ are applied on an object of mass $1 \,kg$ at rest at the origin. The position of the object at $t=2 \,s$ will be:

$A$ spring is compressed between two toy carts of masses $m_1$ and $m_2$. When the toy carts are released,the spring exerts an equal and opposite force on each cart for the same time $t$. If the coefficient of friction $\mu$ between the ground and the carts is the same,find the ratio of the displacements of the two toy carts.

Imagine a situation in which the horizontal surface of block $M_0$ is smooth and its vertical surface is rough with a coefficient of friction $\mu$. In the above problem,choose the correct value$(s)$ of $F$ for which the blocks $M$ and $m$ remain stationary with respect to $M_0$.

$A$ ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards the right as shown. Relative to its initial position with respect to the table,the ball:
$(A)$ Remains stationary if there is no friction between the paper and the ball.
$(B)$ Moves to the left and starts rolling backwards,$i.e.$,to the left if there is friction between the paper and the ball.
$(C)$ Moves forward,$i.e.$,in the direction in which the paper is pulled.
Which of the following statements is/are correct?

Fill in the blanks:
$(a)$ The friction acting on both wheels of a moving bicycle is in the ..... direction.
$(b)$ Friction depends on the ........... and ........ of the contact surfaces.
$(c)$ The necessary condition for parking a vehicle on a banked,curved road is ...........
$(d)$ The time rate of change of momentum gives the physical quantity ...........