A block of mass m slides on the wooden wedge, which in turn slides backwards on the horizontal surface. The acceleration of the block with respect to the wedge is: Given m = 8 kg, M = 16 kg Assume all the surfaces shown in the figure to be frictionless.

Engineering

Physics

Newtons Second Law of Motion

Question

A block of mass m slides on the wooden wedge, which in turn slides backwards on the horizontal surface. The acceleration of the block with respect to the wedge is: Given m = 8 kg, M = 16 kg Assume all the surfaces shown in the figure to be frictionless.

A

$\frac{4}{3} g$

B

$\frac{3}{5} g$

C

$\frac{6}{5} g$

D

$\frac{2}{3} g$

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N cos 60º = Ma₁ = 16 a₁

⇒ N = 32 a₁

$⊥$ to incline

$N = 8 gcos 30 º - 8 a_{1} \sin 30 º \Rightarrow 32 a_{1} = 44 \sqrt{3} g - 4 a_{1}$

$\Rightarrow a_{2} = \frac{\sqrt{3}}{9} g$

Alone incline

8 g sin 30° + 8a₁ cos 30° = ma₂ = 8a₂

$a_{2} = g \times \frac{1}{2} + \frac{\sqrt{3}}{9} g . \frac{\sqrt{3}}{2} = \frac{2 g}{3}$

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