Question

A conveyor belt is moving at a constant speed of $2\text{m/s}$. A box is gently dropped on it. The coefficient of friction between them is $\mu =0.5$. The distance that the box will move relative to belt before coming to rest on it, (taking $g=10{\text{ms}}^2$), is :

• A. $\text{zero}$
• B. $\text{0.6 m}$
• C. $\text{1.2 m}$
• D. $\text{0.4 m}$

Answer 1

The correct option is D $\text{0.4 m}$

Given: $\mu =0.5,u=2\text{m/s}$


When box will come in contact,

$F=ma=\mu N$

$\Rightarrow ma=\mu mg$

$\Rightarrow a=\mu g=0.5\times 10$

$\therefore a=5{\text{m/s}}^2$

From the equation of motion,

$v^2=u^2+2as$
$0=2^2+2\times \left(5\right)s$
$s=-\frac{2}{5}$ w.r.t. belt
or distance $=0.4\text{m}$

Hence, $\left(D\right)$ is the correct answer.