If $300\,J$ of work is done to move a $2\,kg$ block up a rough inclined plane to a height of $10\,m$,find the work done against friction in $J$. (Take $g = 10\,m/s^2$)

$A$ body is sliding down a rough inclined plane. The coefficient of friction between the body and the plane is $0.5$. The ratio of the net force required for the body to slide down and the normal reaction on the body is $1:2$. Then the angle of the inclined plane is (in $^{\circ}$)

$A$ block of mass $4 \ kg$ is at rest on a rough inclined plane making an angle of $\theta$ with the horizontal. The coefficient of static friction between the block and the plane is $0.5$ and the frictional force on the block is $14.14 \ N$. Find the value of $\theta$. (in $^{\circ}$)

$A$ person climbs up a conveyor belt with a constant acceleration. The speed of the belt is $\sqrt{\frac{g h}{6}}$ and the coefficient of friction is $\frac{5}{3 \sqrt{3}}$. The time taken by the person to reach from $A$ to $B$ with the maximum possible acceleration is

$A$ cube of side length $a$ is resting on an inclined plane. What must be the value of the coefficient of friction $\mu$ between the cube and the plane so that the cube topples before sliding?

$A$ child weighing $25$ kg slides down a rope hanging from the branch of a tall tree. If the force of friction acting against him is $2$ $N$,the acceleration of the child is ........ $m/s^2$. (Take $g = 9.8$ $m/s^2$)