First slide

Static friction

Question

A block of mass m is placed on a wedge of mass 2 m which rests on a rough horizontal surface. There is no friction between the block and the wedge. The minimum coefficient of friction between the wedge and the ground, so that the wedge does not move, is

Moderate

A

0.1
B

0.2
C

0.3
D

0.4

Solution

For block, $a = g \sin θ = \frac{g}{\sqrt{2}}$
$a_{H} = a_{V} = a \cos 45 °$
$= \frac{g}{\sqrt{2}} \times \frac{1}{\sqrt{2}} = \frac{g}{2}$
$\frac{N}{\sqrt{2}} = \frac{m g}{2}$ ……..(i)
$m g - \frac{N}{\sqrt{2}} = \frac{m g}{2}$ ……..(ii)
For wedge,
$N^{'} = \frac{N}{\sqrt{2}} + 2 m g$ ……..(iii)
$μ N^{'} = \frac{N}{\sqrt{2}}$ …….(iv)
Solving above four equations, we get
$μ$ =0.2

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