Question

Three blocks of masses $6$ kg, $4$kg & $2$ kg are pulled on a rough surface by applying a constant force $20$N. The values of coefficient of friction between blocks & surface are shown in figure.
In the arrangement shown tension in the string connecting $4$kg and $6$kg masses is?

• A. $8$N
• B. $12$N
• C. $6$N
• D. $4$N

Answer 1

The correct option is A $8$N

Maximum friction force that can act $f_{max}=\mu (N_1+N_2+N_3)$

$⟹f_{max}=\mu (m_1+m_2+m_3)g=0.2(6+4+2)\times 10=24N$

Since $F=20N<f_{max}$, hence body will not move.

For equilibrium of $m_1$ -

$T_1=F-f_1=F-\mu m_{1}g=20-0.2\times 2\times 10=16N$

For equilibrium of $m_2$-

$T_2=T_1-f_2=T_1-\mu m_{2}g=16-0.2\times 4\times 10=8N$

Hence tension in the string between $4kg$ and $6kg$ body is $8N$.

Answer-(A)