NEET-XII-Physics
11: Gravitation
- #19-aFind the magnitude of the gravitational force acting on a particle of mass 2 kg placed at the origin. (b) Find the potential at the points (12 m, 0) and (0, 5 m) if the potential at the origin is taken to be zero. (c) Find the change in gravitational potential energy if a particle of mass 2 kg is taken from the origin to the point (12 m, 5 m). (d) Find the change in potential energy if the particle is taken from (12 m, 0) to (0, 5 m). (b) Find the potential at the points (12 m, 0) and (0, 5 m) if the potential at the origin is taken to be zero. (c) Find the change in gravitational potential energy if a particle of mass 2 kg is taken from the origin to the point (12 m, 5 m). (d) Find the change in potential energy if the particle is taken from (12 m, 0) to (0, 5 m).Ans : `` \stackrel{\to }{\,\mathrm{\,F\,}}=m\stackrel{\to }{\,\mathrm{\,E\,}}``
`` =2\,\mathrm{\,kg\,}\left[\left(5\,\mathrm{\,N\,}/\,\mathrm{\,kg\,}\right)\stackrel{‸}{i}+\left(12\,\mathrm{\,N\,}/\,\mathrm{\,Kg\,}\right)\stackrel{‸}{j}\right]``
`` =\left(10\,\mathrm{\,N\,}\right)\stackrel{‸}{i}+\left(24\,\mathrm{\,N\,}\right)\stackrel{‸}{j}``
`` \therefore \left|\stackrel{\to }{\,\mathrm{\,F\,}}\right|=\sqrt{100+576}=\sqrt{676}=26\,\mathrm{\,N\,}`` (b) `` V=-\stackrel{\to }{\,\mathrm{\,E\,}.}\stackrel{\to }{r}``
Potential at (12 m, 0)`` =-60\,\mathrm{\,J\,}/\,\mathrm{\,Kg\,}``
Potential at (0, 5 m) = `` -60\,\mathrm{\,J\,}/\,\mathrm{\,kg\,}`` (c) change in potential=final potential -initial potential
initial potential=potential at the origin=0
final potential=potential at (12,5)
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{V}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\stackrel{\to }{E}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\stackrel{\to }{r}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{10}\stackrel{‸}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{24}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{120}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{120}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{\text{J}}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{240}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{\text{J}}`` (d) `` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{V}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\stackrel{\to }{E}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\stackrel{\to }{r}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\stackrel{\to }{r}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{0}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{0}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{V}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{10}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{0}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{\text{J}}``
Page No 227: (b) `` V=-\stackrel{\to }{\,\mathrm{\,E\,}.}\stackrel{\to }{r}``
Potential at (12 m, 0)`` =-60\,\mathrm{\,J\,}/\,\mathrm{\,Kg\,}``
Potential at (0, 5 m) = `` -60\,\mathrm{\,J\,}/\,\mathrm{\,kg\,}`` (c) change in potential=final potential -initial potential
initial potential=potential at the origin=0
final potential=potential at (12,5)
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{V}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\stackrel{\to }{E}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\stackrel{\to }{r}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{10}\stackrel{‸}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{24}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{120}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{120}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{\text{J}}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{240}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{\text{J}}`` (d) `` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{V}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\stackrel{\to }{E}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\stackrel{\to }{r}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\stackrel{\to }{r}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{0}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{0}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{V}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{10}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{0}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{\text{J}}``
Page No 227:
- #19-bFind the potential at the points (12 m, 0) and (0, 5 m) if the potential at the origin is taken to be zero.Ans : `` V=-\stackrel{\to }{\,\mathrm{\,E\,}.}\stackrel{\to }{r}``
Potential at (12 m, 0)`` =-60\,\mathrm{\,J\,}/\,\mathrm{\,Kg\,}``
Potential at (0, 5 m) = `` -60\,\mathrm{\,J\,}/\,\mathrm{\,kg\,}``
- #19-cFind the change in gravitational potential energy if a particle of mass 2 kg is taken from the origin to the point (12 m, 5 m).Ans : change in potential=final potential -initial potential
initial potential=potential at the origin=0
final potential=potential at (12,5)
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{V}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\stackrel{\to }{E}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\stackrel{\to }{r}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{10}\stackrel{‸}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{24}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{120}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{120}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{\text{J}}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{240}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{\text{J}}``
- #19-dFind the change in potential energy if the particle is taken from (12 m, 0) to (0, 5 m).Ans : `` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{V}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\stackrel{\to }{E}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\stackrel{\to }{r}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\stackrel{\to }{r}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{0}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{0}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{∆}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{V}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{10}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{+}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{.}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{(}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{12}\stackrel{⏜}{i}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{-}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{5}\stackrel{⏜}{j}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{)}``
`` \textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{=}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{0}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{}\textcolor[rgb]{0.09803921568627451,0.09803921568627451,0.09803921568627451}{\text{J}}``
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