Two masses $A$ and $B$ of $10\,kg$ and $5\,kg$ respectively are connected by a string passing over a frictionless pulley fixed at the corner of a table. The coefficient of friction between mass $A$ and the table is $0.2$. The minimum mass of $C$ that must be placed on $A$ to prevent it from moving is equal to $...........\,kg$.

$A$ 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:

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

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 $cm$?

$A$ uniform wooden stick of mass $1.6 \,kg$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h$ < $l$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. Find the ratio $h/l$ and the frictional force $f$ at the bottom of the stick. $(g=10 \,m \,s^{-2})$

An object of mass $m$ is being moved with a constant velocity under the action of an applied force of $2\, N$ along a frictionless surface with the following surface profile. The correct applied force vs distance graph will be: