Question

For the figure shown below, the coefficient of friction between $2kg$ and $4kg$ block is $0.1$ and between $4kg$ and ground is $0.2$. The graph of friction force acting on $4kg$ block by the ground as a function of time is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A


$f_{1max}={\mu }_1{N}_1=0.1\times 2g=2\text{N}$
$f_{2max}={\mu }_2{N}_2=0.2\times 6g=12\text{N}$


For $0<F<2\text{N}$:
$f_1=F$
i.e Tension will be zero
and $f_2=f_1$
$\therefore f_2=0\to 2\text{N}$ (rightward)

For $2\text{N}<F<4\text{N}$:
$F=f_{1max}+T$
i.e Tension is $0<T<2\text{N}$.
$f_2=f_{1max}-T=2-T$
$\therefore f_2=2\to 0\text{N}$ (rightward)


For $4\text{N}<F<16\text{N}$:
$F=f_{1max}+T$
i.e tension $T$ will be $2\text{N}<T<14\text{N}$
$f_2=T-f_{1max}=T-2$
$\therefore f_2=0\to 12\text{N}$ (leftward)


For $F>16\text{N}$:
Lower block will start moving since $T>f_{1max}+f_{2max}$. Hence friction will be kinetic (constant) and act leftward.

Graph (a) matches these values.