What is the acceleration of the block and trolley system shown in the figure,if the coefficient of kinetic friction between the trolley and the surface is $0.04$? What is the tension in the string? (Take $g = 10\; m s^{-2}$). Neglect the mass of the string.

$A$ 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:

$A$ mass $m$ is tied to one end of a spring and whirled in a horizontal circle with constant angular velocity. The elongation in the spring is $1 \ cm$. If the angular speed is doubled,the elongation in the spring is $6 \ cm$. The original length of the spring is (in $cm$)

$A$ disc of mass $100 \,g$ slides down from rest on an inclined plane of $30^{\circ}$ and comes to rest after travelling a distance of $1 \,m$ along the horizontal plane. If the coefficient of friction is $0.2$ for both inclined and horizontal planes, then the work done by the frictional force over the whole journey, approximately, is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,J$)

$A$ block is placed on a rough horizontal plane. $A$ time-dependent horizontal force $F = Kt$ acts on the block,where $K$ is a positive constant. The acceleration-time graph of the block is:

$A$ string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by