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6.System of Particles and Rotational Motion
hard
$20\;cm$ ત્રિજ્યા અને $0.5\;kg$ દળ ધરાવતી તકતી ઢાળ પર ગબડે છે. તેને ગબડવા માટે જરૂરી ઘર્ષણબળ શોધો.
A
$\frac{5 \sqrt{2}}{3} N$
B
$\frac{5}{3 \sqrt{2}} N$
C
$\frac{5}{\sqrt{2}} N$
D
$\frac{5}{2 \sqrt{3}} N$
(AIIMS-2019)
Solution
Consider the following figure.
From the above figure,
$Mg \sin \theta- f = ma _{ cm }$
As we know that,
$\tau_{ cm }= I _{ cm } \alpha$
And,
$f =\frac{ MR ^{2}}{2}\left(\frac{ a _{ cm }}{ R ^{2}}\right)$
$=\frac{ Ma _{ cm }}{2}$
$a_{c m}=\frac{2 f_{R}}{M}$
Therefore,
$mg \sin \theta- f = M \left(\frac{2 f }{ M }\right)$
$f =\frac{ mg \sin \theta}{3}$
Substitute the values.
$f =\frac{1}{2}\left(\frac{10}{3}\right)\left(\frac{1}{\sqrt{2}}\right)$
$=\frac{5}{3 \sqrt{2}} N$
Standard 11
Physics
