Two masses m and M are attached to the strings as shown in the fi… - Vidyadip

MCQ

Two masses $m$ and $M$ are attached to the strings as shown in the figure. If the system is in equilibrium, then

✓
$tan\theta = 1 +\frac{{2M}}{m}$
B
$cot\theta = 1 + \frac{{2M}}{m}$
C
$tan\theta = 1 + \frac{{2M}}{m}$
D
$cot\theta = 1 + \frac{{2M}}{m}$

✓

Answer

Correct option: A.

$tan\theta = 1 +\frac{{2M}}{m}$

a
$m g=2 T \sin 45^{\circ}$

$m g=\sqrt{2 T}$

$T_{1} \cos \theta=T \cos 45^{\circ}$

$T_{1} \cos \theta=\frac{T}{\sqrt{2}}=\frac{m g}{2}$

$\left\{T=\frac{m g}{\sqrt{2}}\right\}$

Further, $M g+T \cos 45^{\circ}=T_{1} \sin \theta$

$T_{1} \sin \theta=M g+\frac{M g}{\sqrt{2}} \frac{1}{\sqrt{2}}$

$T_{1} \sin \theta=M g+\frac{m g}{2}$

$\tan \theta=\frac{M g+\frac{m g}{2}}{\frac{M g}{2}}=1+\frac{2M}{m}$

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