An open knife edge of mass $m$ is dropped from a height $h$ on a wooden floor. If the blade penetrates up to the depth $d$ into the wood,the average resistance offered by the wood to the knife edge is

$A$ small bob $A$ of mass $m$ is attached to a massless rigid rod of length $1 \ m$ pivoted at point $P$ and kept at an angle of $60^{\circ}$ with the vertical as shown in the figure. At a distance of $1 \ m$ below point $P$,an identical bob $B$ is kept at rest on a smooth horizontal surface that extends to a circular track of radius $R$ as shown in the figure. If bob $B$ just manages to complete the circular path of radius $R$ up to a point $Q$ after being hit elastically by bob $A$,then the radius $R$ is . . . . . . $m$.

$A$ particle of mass $m$ moving horizontally with velocity $v_0$ strikes a smooth wedge of mass $M$,as shown in the figure. After the collision,the particle starts moving up the inclined face of the wedge and rises to a height $h$. The maximum height $h$ attained by the particle is:

$A$ bullet of mass $m_1$ is moving with speed $v_0$ and hits a sand bag of mass $m_2$. If the speed of the bullet after passing through the sand bag is $\frac{v_0}{3}$,then the height $h$ up to which the bag rises is (assume,$g=$ acceleration due to gravity).

$A$ man of mass $60 \ kg$ gets $10^5 \ calories$ of energy from food. If his efficiency is $28\%$,up to what height in $m$ can he climb?

$A$ block of mass $5 \,kg$ is moved by a distance of $10 \,m$ on a surface with a coefficient of friction $\mu = 0.2$ by applying a force of $25 \,N$. The kinetic energy gained by the block is ...... $J$. (Take $g = 10 \,m/s^2$)