A block of mass m1 is resting on a rough horizontal plane- coefficient of kinetic friction between block and surface is - If m1 is connected to another mass m2 with the help of string and pulley as shown in figure- then the common acceleration when the system is released from rest will be -

The correct option is D [ m_2 μ m_1/m_1+ m_2 ]g Given, #10; #10;Coefficient #10;of friction =μ #10; #10;Tension in string #10; T=m_2 ...

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Byju's Answer

Standard XII

Physics

Friction General Understanding

A block of ma...

Question

A block of mass $m_{1}$ is resting on a rough horizontal plane, coefficient of kinetic friction between block and surface is $μ$ . If $m_{1}$ is connected to another mass $m_{2}$ with the help of string and pulley as shown in figure, then the common acceleration when the system is released from rest will be :

\frac{m_{2} g}{m_{1} + m_{2}}

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[\frac{m_{2} - m_{1}}{m_{1} + μ m_{2}}] g

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\frac{μ (m_{2} + m_{1})}{m_{1} + m_{2}} g

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[\frac{m_{2} - μ m_{1}}{m_{1} + m_{2}}] g

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Solution

The correct option is D $[\frac{m_{2} - μ m_{1}}{m_{1} + m_{2}}] g$
Given,

Coefficient of friction $= μ$

Tension in string $T = m_{2} g$

Friction force $F_{r} = μ m_{1} g$

Resultant force give acceleration $a$ to the system

$(m_{1} + m_{2}) a = m_{2} g - F_{r}$

$\Rightarrow (m_{1} + m_{2}) a = m_{2} g - μ m_{1} g$

$\Rightarrow a = \frac{m_{2} g - μ m_{1} g}{m_{1} + m_{2}}$

Acceleration of system is $a = [\frac{m_{2} - μ m_{1}}{m_{1} + m_{2}}] g$

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