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  4. Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m2 to stop the motion is -

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Q. Two masses $m_1 = 5\, kg$ and $m_2 = 10\, kg$, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. 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 -Physics Question Image

JEE MainJEE Main 2018Laws of Motion

Solution:

To stop the moving block $m_{2}$, acceleration of $m_{2}$ should be opposite to velocity of $m_{2}$
$m_{1} g<\mu\left(m+m_{2}\right) g$
$\Rightarrow 5<0.15\left(10+m_{2}\right)$
$\Rightarrow m_{2}>23.33\, kg$
$\therefore $ Minimum mass $=27.3\, kg$ (according to given options)