$A$ block is kept on a rough horizontal surface. The acceleration of the block increases from $6 \ m/s^2$ to $11 \ m/s^2$ when the horizontal force acting on it increases from $20 \ N$ to $30 \ N$. The coefficient of kinetic friction between the block and the surface is (Acceleration due to gravity $g = 10 \ m/s^2$):

It is difficult to move a cycle with brakes on because

When the engine is switched off, a vehicle of mass $M$ is moving on a rough horizontal road with momentum $p$. If the coefficient of friction between the road and the tyres of the vehicle is $\mu_k$, what is the distance travelled by the vehicle before it comes to rest?

$A$ uniform rope of total length $l$ is at rest on a table with a fraction $f$ of its length hanging (see figure). If the coefficient of friction between the table and the rope is $\mu$,then:

$A$ man of mass $60 \, kg$ slides down a pole by applying a force of $600 \, N$ on it. If the coefficient of friction between the hands and the pole is $0.5$,then the acceleration of the man is ............ $m/s^2$ $(g = 10 \, m/s^2)$.

$A$ block of mass $m=2 \ kg$ is initially at rest on a horizontal surface. $A$ horizontal force $F_1=(6 \ N) \hat{i}$ and a vertical force $F_2=(10 \ N) \hat{j}$ are then applied to the block. The coefficients of static friction and kinetic friction for the block and the surface are $0.4$ and $0.25$, respectively. The magnitude of the frictional force acting on the block is (assume $g=10 \ m/s^2$): (in $N$)