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7.Gravitation
normal
પૃથ્વીનું દળ અચળ રાખીને ત્રિજયા $\frac{1}{n}$ ભાગની કરતાં $1$ દિવસ કેટલો થાય?
A
$\frac{{24}}{n}\,hr$
B
$\frac{{24}}{{{n^2}}}\,hr$
C
$24\,n\,\,\,hr$
D
$24\,{n^2}\,\,\,hr$
Solution
$L = I\omega $
$ = \frac{2}{5}M{R^2} \times \frac{{2\pi }}{T} = $ constant
$T \propto {R^2}$
$⇒ \frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{R_2}}}{{{R_1}}}} \right)^2}$
$ = {\left( {\frac{{R/n}}{R}} \right)^2}$
$ = \frac{1}{{{n^2}}}$
$⇒ {T_2} = \frac{{24}}{{{n^2}}}hr$ [${T_1} = 24\,hr$]
Standard 11
Physics
