If a pushing force making an angle α with horizontal is applied on a block of mass m placed on hori

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4-1.Newton's Laws of Motion

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If a pushing force making an angle $\alpha$ with horizontal is applied on a block of mass $m$ placed on horizontal table and angle of friction is $\beta$, then minimum magnitude of force required to move the block is

A

$\frac{m g \sin \beta}{\cos [\alpha-\beta]}$

B

$\frac{m g \sin \beta}{\cos [\alpha+\beta]}$

C

$\frac{m g \sin \beta}{\sin [\alpha+\beta]}$

D

$\frac{m g \cos \beta}{\cos [\alpha-\beta]}$

Solution

(b)

Angle of friction is $\beta$

$\Rightarrow \mu=\tan \beta$

$N=m g+F \sin \alpha$

To just move the block

$F \cos \alpha=\mu N$

$F \cos \alpha=\tan \beta(m g+F \sin \alpha)$

$F(\cos \alpha-\tan \beta \sin \alpha)=m g \tan \beta$

$F(\cos \alpha \cos \beta-\sin \alpha \sin \beta)=m g \sin \beta$

$F=\frac{m g \sin \beta}{\cos (\alpha+\beta)}$

Standard 11

Physics

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