Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{{3{t^2}}}{2}$ $W$. Here $t$ is in $seconds$ . If velocity of particle at $t = 0$ is $v = 0$. The velocity of particle at time $t = 2\, sec$. will be ........... $\mathrm{m}/ \mathrm{s}$
$1$
$4$
$2$
$2\sqrt 2$
A car is moving on a straight horizontal road with a speed $v.$ If the coefficient of friction between the tyres and the road is $\mu ,$ the shortest distance in which the car can be stopped is
Answer carefully, with reasons :
$(a)$ In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ?
$(b)$ Is the total linear momentum conserved during the short time of an elastic collision of two balls ?
$(c)$ What are the answers to $(a)$ and $(b)$ for an inelastic collision ?
$(d)$ If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ?
(Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).
If the potential energy of a gas molecule is $U = \frac{M}{{{r^6}}} - \frac{N}{{{r^{12}}}},M$ and $N$ being positive constants, then the potential energy at equilibrium must be
$A$ & $B$ are blocks of same mass $m$ exactly equivalent to each other. Both are placed on frictionless surface connected by one spring. Natural length of spring is $L$ and force constant $K$. Initially spring is in natural length. Another equivalent block $C$ of mass $m$ travelling at speed $v$ along line joining $A$ & $B$ collide with $A$. In ideal condition maximum compression of spring 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 $g = 10\,m/s^2$ )