What is the minimum value of F needed so that block begins to mov… - Vidyadip

MCQ

What is the minimum value of $F$ needed so that block begins to move upward on frictionless incline plane as shown

✓
$M g \tan \left(\frac{\theta}{2}\right)$
B
$M g \cot \left(\frac{\theta}{2}\right)$
C
$\frac{M g \sin \theta}{(1+\sin \theta)}$
D
$M g \sin \left(\frac{\theta}{2}\right)$

✓

Answer

Correct option: A.

$M g \tan \left(\frac{\theta}{2}\right)$

a
(a)

$F+F \cos \theta=m g \sin \theta$

$F=\frac{m g \sin \theta}{1+\cos \theta}$

$F=\frac{m g 2 \sin \frac{\theta}{2} \cos \frac{\theta}{2}}{2 \cos ^2 \frac{\theta}{2}}$ $\left(\because \sin \theta=2 \sin \frac{\theta}{2} \cdot \cos \frac{\theta}{2}\right.$ and $\left.1+\cos \theta=2 \cos ^2 \frac{\theta}{2}\right)$

$=m g \tan \frac{\theta}{2}$

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