$A$ person used force $(F)$,shown in the figure,to move a load with a constant velocity on a given surface. Identify the correct surface profile.

$A$ sphere is placed rotating with its centre initially at rest in a corner as shown in figures $(a)$ and $(b)$. The coefficient of friction between all surfaces and the sphere is $\mu = \frac{1}{3}$. Find the ratio of the frictional force $\frac{f_a}{f_b}$ exerted by the ground in situations $(a)$ and $(b)$.

Two carts of masses $200 \, kg$ and $300 \, kg$ on horizontal rails are pushed apart. Suppose the coefficient of friction between the carts and the rails is the same. If the $200 \, kg$ cart travels a distance of $36 \, m$ and stops,then the distance travelled by the cart weighing $300 \, kg$ is ........ $m$.

$A$ cone of radius $r$ and height $h$ rests on a rough horizontal surface. The coefficient of friction between the cone and the surface is $\mu$. $A$ gradually increasing horizontal force $F$ is applied to the vertex of the cone. The largest value of $\mu$ for which the cone will slide before it topples is

Three blocks $A, B$ and $C,$ of masses $4 \, kg, 2 \, kg$ and $1 \, kg$ respectively,are in contact on a frictionless surface,as shown. If a force of $14 \, N$ is applied on the $4 \, kg$ block,then the contact force between $A$ and $B$ is .......... $N$.

$A$ body of mass $m = 10^{-2} \ kg$ is moving in a medium and experiences a frictional force $F = -kv^2$. Its initial speed is $v_0 = 10 \ ms^{-1}$. If,after $10 \ s$,its energy is $\frac{1}{8} mv_0^2$,the value of $k$ will be