A particle is moved from $(0, 0)$ to $(a, a)$ under a force $\vec F = (3\hat i + 4\hat j)$ from two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the work done by this force in these two paths respectively. Then
$W_1 = W_2$
$W_1 = 2W_2$
$W_2 = 2W_1$
$W_2 = 4W_1$
$A$ man who is running has half the kinetic energy of the boy of half his mass. The man speeds up by $1 \, m/s$ and then has the same kinetic energy as the boy. The original speed of the man was
A particle fall from height $h$ on $a$ static horizontal plane rebounds. If $e$ is coefficient of restitution then before coming to rest the total distance travelled during rebounds will be:-
After head on elastic collision between two balls of equal masses , one is observed to have a speed of $3\,\,m/s$ along positive $x-$ axis and the other has a speed of $2\,\,m/s$ along negative $x$ axis. The original velocities of the balls are
Two bodies of masses $0.1\, kg$ and $0.4\, kg$ move towards each other with the velocities $1\, m/s$ and $0.1\, m/s$ respectively. After collision they stick together. In $10\, sec$ the combined mass travels ............... $\mathrm{m}$
A body moving with speed $v$ in space explodes into two piece of masses in the ratio $1 : 3.$ If the smaller piece comes to rest, the speed of the other piece is