First slide

Mechanical equilibrium force cases

Question

A sphere of mass m is held between two smooth inclined walls. For sin37° = $\frac{3}{5}$ , the normal reaction of the wall (2) is equal to

Moderate

A

$\frac{16 m g}{25}$
B

$\frac{25 m g}{39}$
C

$\frac{39 m g}{21}$
D

None of these

Solution

$N_{1} \sin 37 ° = N_{2} \sin 74 °$
$\Rightarrow N_{1} = 2 N_{2} \cos 37 °$
Now, $N_{1} \cos 37 ° - N_{2} \cos 74 ° = m g$
$\Rightarrow 2 N_{2} \cos^{2} 37 ° - N_{2} (2 \cos^{2} 37 ° - 1) = m g$
$\Rightarrow 2 N_{2} (\frac{16}{25}) - N_{2} (\frac{32}{25} - 1) = m g \Rightarrow N_{2} = m g$

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