Question

In the figure shown below, a horizontal force $F$ is applied on $6kg$ block towards left. If the coefficients of friction between the surfaces are $0.3$ and $0.4$ as shown in the figure. then the value of tension in the rope and force required just to slide the $6kg$ block under the $3kg$ block is (Take $g=10m/s^2$)

• A. $T=3\text{N},F=40\text{N}$
• B. $T=6\text{N},F=45\text{N}$
• C. $T=9\text{N},F=45\text{N}$
• D. $T=9\text{N},F=40\text{N}$

Answer 1

The correct option is C $T=9\text{N},F=45\text{N}$

As per the question, the block of mass $6kg$ will just slide under block of mass $3kg$. Then, the condition of friction will be limiting.

The FBDs of the blocks are as shown


At equilibrium, we have
$N_1=3g=30\text{N}$
$f_1=T$
In limiting case, $f_1={\mu }_1{N}_1=0.3\times 30=9\text{N}$ $\Rightarrow T=9\text{N}$

Again, from the FBD of $6kg$ block, we have
$N_2=N_1+6g=30+60=90\text{N}$
$F=f_1+f_2$
In limiting case, $f_2={\mu }_2{N}_2=0.4\times 90=36\text{N}$
$\Rightarrow F=9+36=45\text{N}$