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6.System of Particles and Rotational Motion
medium
A physical balance has its arms of unequal length. A body weighs $18 \,kg$ if kept in one pan and weighs $8 \,kg$ if kept in the other pan. The true weight of the body is ............. $kg$
A$13$
B$12$
C$10$
D$16$
Solution
(b)
Case$-I$
Clockwise moment $=W \times L_1$
anticlock wise moment $=18 \times L_2$
$\Rightarrow L_1=18 \times L_2$
$\Rightarrow \frac{L_1}{L_2}=\frac{18}{\omega}$
Similarly,
Care $- II$
$W \times L_2=8 \times L_1$
$\Rightarrow \frac{L_1}{L_2}=\frac{W}{8}$
equating $(i)$ and $(III)$
$\omega^2=18 \times 8=144$
$\Rightarrow \omega=\sqrt{144}=12\,kg$
Case$-I$
Clockwise moment $=W \times L_1$
anticlock wise moment $=18 \times L_2$
$\Rightarrow L_1=18 \times L_2$
$\Rightarrow \frac{L_1}{L_2}=\frac{18}{\omega}$
Similarly,
Care $- II$
$W \times L_2=8 \times L_1$
$\Rightarrow \frac{L_1}{L_2}=\frac{W}{8}$
equating $(i)$ and $(III)$
$\omega^2=18 \times 8=144$
$\Rightarrow \omega=\sqrt{144}=12\,kg$
Standard 11
Physics