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 body of mass $M$ is dropped from a height $h$ on a sand floor. If the body penetrates $x\,\,cm$ into the sand, the average resistance offered by the sand of the body is
A wooden block of mass $M$ is suspended by a cord and is at rest. A bullet of mass $m,$ moving with a velocity $v$ passes through the block and comes out with a velocity $v/2$ in the same direction. If there is no loss in kinetic energy, then upto what height the block will rise
A mass $m$ slips along the wall of a semispherical surface of radius $R$. The velocity at the bottom of the surface is
A 3.628 kg freight car moving along a horizontal rail road spur track at $7.2\; km/hour$ strikes a bumper whose coil springs experiences a maximum compression of $30 \;cm$ in stopping the car. The elastic potential energy of the springs at the instant when they are compressed $15\; cm$ is [2013]
(a) $12.1 \times 10^4\;J$ (b) $121 \times 10^4\;J$ (c) $1.21 \times 10^4\;J$ (d) $1.21 \times 10^4\;J$
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