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
$\frac{{{{({a^2} + {b^2})}^{1/2}}}}{m}$
$\frac{{{a^2} + {b^2}}}{m}$
$\frac{{{{(a + b)}^{1/2}}}}{m}$
$\frac{{a + b}}{m}$
A force $\overrightarrow F = (5\hat i + 3\hat j)$Newton is applied over a particle which displaces it from its origin to the point $\overrightarrow r = (2\hat i - 1\hat j)$ metres. The work done on the particle is..............$J$
A ball after falling from a height of $10\, m$ strikes the roof of a lift which is descending down with a velocity of $1\, m/s$. The recoil velocity of the ball will be .............. $\mathrm{m}/ \mathrm{s}$
A particle moves along the $x-$ axis from $x = 0$ to $x = 5\,m$ under the influence of a force $F$ (in $N$ ) given by $F = 3x^2 -2x + 7$ . Calculate the work done by this force .............. $\mathrm{J}$
A vertical spring with force constant $k$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is
The force $F$ acting on a body moving in a circle of radius $r$ is always perpendicular to the instantaneous velocity $v$. The work done by the force on the body in one complete rotation is :