An open knife edge of mass $50 \ g$ is dropped from a height $2 \ m$ on a wooden floor. If the blade penetrates up to a depth of $10 \ cm$ into the wood,the average resistance offered by the wood to the knife edge is $....N$

$A$ force acts on a $2\,kg$ object so that its position is given as a function of time as $x = 3t^2 + 5$. What is the work done by this force in the first $5\,seconds$? ................ $J$

$A$ simple pendulum is released from $A$ as shown in the figure. If $m$ and $l$ represent the mass of the bob and the length of the pendulum respectively,the gain in kinetic energy at $B$ is

An unloaded bus can be stopped by applying brakes on a straight road after covering a distance $x$. Suppose the passengers add $50 \%$ of its weight as the load and the braking force remains unchanged,how far will the bus go after the application of the brakes? (Velocity of the bus in both cases is the same.)

$A$ body falls freely under gravity. Its speed is $v$ when it has lost an amount $U$ of the gravitational potential energy. Then its mass is

State the principle of conservation of mechanical energy for a conservative force.