First slide

Static friction

Question

A block of mass M₁ = 10 kg is placed on a slab of mass M₂ =30kg, The slab lies on a frictionless horizontal surface as shown in fig. The coefficient of static
friction between the block and slab is µ₁ =0.5 and that of dynamic friction is µ₂ =0.15.A force F =40N acts on block M₁. What will be the acceleration with which the slab will move? $(Take g = 10 m / s^{2})$

Moderate

A

5 m/s²
B

2 m/s²
C

1 m/s²
D

zero

Solution

The slab will move due to the force exerted on it due to the friction between the block and slab. When the force acting on the block is less than the static friction, it will not move. The total force causing acceleration of M₁ and M₂ both will be the force applied.
Limiting friction $= {μM}_{1} g = 0 \cdot 5 \times 10 \times 10 = 50 N$
So, the applied force will not cause motion of M₁.
$∴$ The acceleration of system
$a = \frac{40 N}{(10 + 30) kg} = 1 m / s^{2}$

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