Question

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

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

Answer 1

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

Force on the block = $mg\sin \theta$
$=1\times 10\times \frac{1}{2}=5N$
Limiting friction = $\mu mg\cos \theta$
$=0.4\times 1\times 10\times \frac{\sqrt{3}}{2}$
$=2\sqrt{3}$
$\approx 3.4N$, as $\sqrt{3}=1.7$ given
$F>f_L$ (body slips)
Net force $\Rightarrow ma=mg\sin \theta -\mu mg\cos \theta$
$\Rightarrow 5-3.4=a$
$a=1.6{\text{m/s}}^2$