A block of mass 2 kg is pushed against a rough vertical wall with a...

A block of mass 2 kg is pushed against a rough vertical wall with a force of 40 N , coefficient of static friction being 0.5. Another horizontal force of 15 N , is applied on the block in a direction parallel to the wall. If the block will move, then its direction would be

Options

A $15^{\circ}$ with 15 N force
B $53^{\circ}$ with 15 N force
C $45^{\circ}$ with 15 N force
D $75^{\circ}$ with 15 N force

Correct answer

B. $53^{\circ}$ with 15 N force

Step-by-step solution

The net force

=\sqrt{20^2+15^2}-0.5 \times 40

\begin{aligned} & =25-20=5 \mathrm{~N} \\ & \therefore \quad \tan \theta=\frac{20}{15}=\frac{4}{3} \\ & \therefore \quad \theta=\tan ^{-1}\left(\frac{4}{3}\right)=53^{\circ} \\ & \end{aligned}

So, the block will move at an angle

53^{\circ}$ with the 15 N force.

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