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In the figure, the coefficient of friction between the floor and the block B is 0.1. The coefficient of friction between the block B and A is 0.2. The mass of B is m and the mass of A is m/2. The maximum horizontal force F that can be applied to the block B, so that both blocks move together is

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0.15 mg

0.25 mg

0.1 mg

0.45 mg

answer is D.

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Detailed Solution

Acceelration of the system

$a = \frac{F - μ_{2} (m_{1} + m_{2}) g}{m_{1} + m_{2}}$

maximum common acceleration

$= \frac{f_{1} max}{m_{1}} = μ_{1} \cdot g$

$F = (μ_{1} + μ_{2}) (m_{1} + m_{2}) g$

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