The potential energy of a body of mass $m$ is:
$U = ax + by$
Where $x$ and $y$ are position co-ordinates of the particle. The acceleration of the particle is
$\frac{{{{({a^2} + {b^2})}^{1/2}}}}{m}$
$\frac{{{a^2} + {b^2}}}{m}$
$\frac{{{{(a + b)}^{1/2}}}}{m}$
$\frac{{a + b}}{m}$
Three particles of masses $10g, 20g$ and $40g$ are moving with velocities $10\widehat i,10\widehat j$ and $10\widehat k$ $m/s$ respectively. If due to some mutual interaction, the first particle comes to rest and the velocity of second particle becomes $\left( {3\widehat i + 4\widehat j\,\,} \right)\, m/s$, then the velocity of third particle is
A particle moves with a velocity $\vec v\, = \,5\hat i - 3\hat j + 6\hat k\,\,m/s$ under the influence of a constant force $\vec F\, = \,10\hat i + 10\hat j + 20\hat k$. Instantaenous power will be ............... $\mathrm{J} / \mathrm{s}$
$A$ ball is dropped from $a$ height $h$. As it bounces off the floor, its speed is $80$ percent of what it was just before it hit the floor. The ball will then rise to $a$ height of most nearly .............. $\mathrm{h}$
A particle of mass $4\, m$ which is at rest explodes into three fragments. Two of the fragments each of mass $m$ are found to move with a speed $v$ each in perpendicular directions. The total energy released in the process will be
If a spring extends by $x$ on loading then energy stored by the spring is ($T$ is tension in spring, $K$ is spring constant)