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4-1.Newton's Laws of Motion
normal
Two masses $m$ and $M$ are attached to the strings as shown in the figure. If the system is in equilibrium, then
A
$tan\theta = 1 +\frac{{2M}}{m}$
B
$cot\theta = 1 + \frac{{2M}}{m}$
C
$tan\theta = 1 + \frac{{2M}}{m}$
D
$cot\theta = 1 + \frac{{2M}}{m}$
Solution
$m g=2 T \sin 45^{\circ}$
$m g=\sqrt{2 T}$
$T_{1} \cos \theta=T \cos 45^{\circ}$
$T_{1} \cos \theta=\frac{T}{\sqrt{2}}=\frac{m g}{2}$
$\left\{T=\frac{m g}{\sqrt{2}}\right\}$
Further, $M g+T \cos 45^{\circ}=T_{1} \sin \theta$
$T_{1} \sin \theta=M g+\frac{M g}{\sqrt{2}} \frac{1}{\sqrt{2}}$
$T_{1} \sin \theta=M g+\frac{m g}{2}$
$\tan \theta=\frac{M g+\frac{m g}{2}}{\frac{M g}{2}}=1+\frac{2M}{m}$
Standard 11
Physics
