When a constant force is applied to a body moving with constant acceleration, power does not remain constant. For power to be constant, the force has to vary with speed as follows
$F \propto \frac{1}{\upsilon }$
$F \propto \frac{1}{\sqrt \upsilon }$
$F \propto {\upsilon }$
$F \propto {\upsilon ^2}$
A shell is fired from a canon with a velocity $V$ at an angle $\theta$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces come to rest. The speed of the other piece immediately after the explosion is
Pulley and spring are massless and the friction is absent everwhere. $5\,kg$ block is released from rest. The speed of $5\,kg$ block when $2\,kg$ block leaves the contact with ground is (take force constant of the spring $K = 40\,N/m$ and $g = 10\,m/s^2$ )
In an elastic collision of two particles the following quantity is conserved
A block of mass $1\,kg$ is pushed up a surface inclined to horizontal at an angle of $30^o$ by a force of $10\,N$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1$. If the block is pushed up by $10\,m$ along the inclined calculate
$(a)$ work done against gravity
$(b)$ work done against force of friction
$(c)$ increases in potential energy
$(d)$ increases in kinetic energy
$(e)$ work done by applied force
A uniform flexible chain of mass $m$ and length $2l$ hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain is given a small vertical displacement so that the chain slips over the pin. The speed of chain when it leaves pin is