Consider a block and trolley system as shown in the figure. If the coefficient of kinetic friction between the trolley and the surface is $0.04$,the acceleration of the system in $m/s^2$ is (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless):

$A$ block of mass $m$ (initially at rest) is sliding up a rough vertical wall with the help of a force $F$ whose magnitude is constant but direction is changing. $\theta = {\theta _0}t$,where $t$ is time in seconds. At $t = 0$,the force is in the vertical upward direction,and as time passes,its direction changes until $\theta = \frac{\pi }{2}$. The value of $F$ such that the block comes to rest when $\theta = \frac{\pi }{2}$ is:

$A$ child weighing $25 \,kg$ slides down a rope hanging from a branch of a tall tree. If the force of friction acting against him is $200 \,N$,the acceleration of the child is ........... $m/s^2$ $\left(g=10 \,m/s^2\right)$.

$A$ body of mass $2 \, kg$ is kept by pressing it against a vertical wall by a force of $100 \, N$. The coefficient of friction between the wall and the body is $0.3$. Then the frictional force is equal to ........ $N$.

$A$ block of mass $10 \, kg$ moving with an acceleration of $2 \, m/s^2$ on a horizontal rough surface is shown in the figure. The value of the coefficient of kinetic friction is ...........

$A$ block of mass $\sqrt{2} \,kg$ is placed on a rough horizontal surface. $A$ force $F$ acting upwards at an angle of $45^{\circ}$ with the horizontal causes the block to start motion. If the coefficient of static friction between the surface and the block is $0.25$, the magnitude of the force $F$ is (Acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,N$)