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Block on a Block Problems

Two masses m1...

Question

Two masses $m_{1} = 5 k g$ and $m_{2} = 10 k g$ connected by an inextensible string over a frictionless pulley, as shown in the figure are moving . The coefficient of friction of horizontal surface is $0.15$ . The minimum weight $m$ that should be put on top of $m_{2}$ to stop the motion is

18.33 k g

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23.33 k g

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43.33 k g

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10.33 k g

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Solution

The correct option is B $23.33 k g$

Motion stops when pull due to $m_{1} \leq$ force of friction between $m_{2}$ and surface.
$\Rightarrow m_{1} g \leq μ (m_{2} + m) g$
$\Rightarrow 5 \times g \leq 0.15 (10 + m) \times g$
$\Rightarrow m \geq 23.33 k g$

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