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$R$ ત્રિજયાના વર્તુળમાં ગતિ કરતા કણની ગતિઊર્જા $k = a{s^2}$ છે.જયાં $s$ એ સ્થાનાંતર છે. તો કણ પર કેટલું બળ લાગતું હશે?
$2a\frac{{{s^2}}}{R}$
$2as{\left( {1 + \frac{{{s^2}}}{{{R^2}}}} \right)^{1/2}}$
$2as$
$2a\;\frac{{{R^2}}}{s}$
Solution
${F_{Net}} = \sqrt {F_c^2 + F_t^2} $ ….(i)
${F_c} = \frac{{m{v^2}}}{R}$$ = \frac{{2a{s^2}}}{R}$ ….(ii) $[\frac{1}{2}m{v^2} = a{s^2} ]$
$\frac{1}{2}m{v^2} = a{s^2}$
$\Rightarrow {v^2} = \frac{{2a{s^2}}}{m}$
$\Rightarrow v = s\sqrt {\frac{{2a}}{m}} $
${a_t} = \frac{{dv}}{{dt}} = \frac{{dv}}{{ds}}\,.\,\frac{{ds}}{{dt}} \,\Rightarrow \,{a_t} = \frac{d}{{ds}}\left[ {s\sqrt {\frac{{2a}}{m}} } \right]\,.v$
$\therefore {a_t} = v\sqrt {\frac{{2a}}{m}} \, = s\sqrt {\frac{{2a}}{m}} \,\sqrt {\frac{{2a}}{m}} \,= \frac{{2as}}{m}$
${F_t} = m{a_t} = 2as$ ….(iii)
$\therefore {F_{Net}} = \sqrt {{{\left( {\frac{{2a{s^2}}}{R}} \right)}^2} + {{\left( {2as} \right)}^2}} $
$\therefore {F_{Net}} = 2as\,{\left[ {1 + \frac{{{s^2}}}{{{R^2}}}} \right]^{1/2}}$
