As shown in the figure,a block of mass $2 \ kg$ is placed on a rough inclined plane such that it just touches the spring. The block moves downwards. What will be the maximum compression of the spring in $cm$?

$A$ particle of mass $m$ falls from rest through a resistive medium having a resistive force, $F = -kv$, where $v$ is the velocity of the particle and $k$ is a constant. Which of the following graphs represents velocity $(v)$ versus time $(t)$?

$A$ heavy ball of mass $M$ is suspended from the ceiling of a car by a light string of mass $m$ $(m \ll M)$. When the car is at rest,the speed of transverse waves in the string is $60 \, ms^{-1}$. When the car has acceleration $a$,the wave-speed increases to $60.5 \, ms^{-1}$. The value of $a$,in terms of gravitational acceleration $g$,is closest to:

In the figure,a block of weight $60 \ N$ is placed on a rough surface. The coefficient of friction between the block and the surface is $0.5$. What should be the maximum weight $W$ (in $N$) such that the block does not slip on the surface?

In the figure,two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with coefficient of friction $\mu$ and the mass $m$ is hanging vertically against a smooth vertical wall. The pulley is frictionless. Imagine a situation in which the given arrangement is placed inside an elevator that can move only in the vertical direction and compare the situation with the case when it is placed on the ground. When the elevator accelerates downward with $a_0 (< g)$,then

$A$ 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.