Question

A block of mass $\text{1 kg}$ is placed on a rough incline as shown. The coefficient of friction between block and incline is $0.4$. The acceleration of block is $(g={\text{10 ms}}^{-2},\sqrt{3}=1.7)$

• A. zero
• B. ${\text{1.6 ms}}^{-2}$
• C. ${\text{6.5 ms}}^{-2}$
• D. ${\text{5 ms}}^{-2}$

Answer 1

The correct option is B ${\text{1.6 ms}}^{-2}$

Applied force on the block is its own weight along the incline
$F=mg\sin \theta$
$=1\times 10\times \frac{1}{2}=5\text{N}$
Limiting friction $f=\mu mg\cos \theta$
$=0.4\times 1\times 10\times \frac{\sqrt{3}}{2}$
$=2\sqrt{3}$
$=\text{3.4 N}$
For $F>f$, body slips
Net force $=mgsin\theta -\mu mg\cos \theta$
$=5-3.4=1.6$
i.e $ma=1.6\text{N}$
$a={\text{1.6 m/s}}^2$