Question

A block of mass $10\text{kg}$ is placed on rough horizontal surface whose coefficient of friction is $0.5$. If a horizontal force of $100\text{N}$ is applied on it, then acceleration of block will be [Take $g=10{\text{ms}}^{-2}$]

• A. $10{\text{ms}}^{-2}$
• B. $5{\text{ms}}^{-2}$
• C. $15{\text{ms}}^{-2}$
• D. $0.5{\text{ms}}^{-2}$

Answer 1

The correct option is B $5{\text{ms}}^{-2}$

By the FBD
$(m=10\text{kg},g=10{\text{ms}}^{-2},\mu =0.5,F=100\text{N})$
Force of friction, $f=\mu N=mg$
$=0.5\times 10\text{kg}\times 10{\text{ms}}^{-2}=50\text{N}$
Force that produces acceleration, $(F$ is the applied force$)$
$F^{\prime }=F-f=100\text{N}-50\text{N}=50\text{N}$
$a=\frac{F^{\prime }}{m}=\frac{50\text{N}}{10\text{kg}}=5{\text{ms}}^{-2}$