Question

Two bodies of masses $1kg$ and $2kg$ are projected with same velocities, on two rough surfaces whose coefficients of friction are $0.2$ and $0.4$ respectively. Find the ratio of distances travelled by them before their velocities become half of the initial value.

• A. $1:3$
• B. $2:1$
• C. $1:4$
• D. $4:1$

Answer 1

The correct option is B $2:1$

The magnitude of $a=\frac{f_k}{m}=\frac{{\mu }_{k}mg}{m}=\mu g$
$\text{Initial velocity}=u,\text{Final velocity}=v=\frac{u}{2}$,
Friction opposes motion, so $a=-\mu g$,
Hence,
$v^2-u^2=2as;{\left(\frac{u}{2}\right)}^2-u^2=-2\mu gs$
$\Rightarrow s=\frac{3u^2}{8\mu g}$
Hence ratio of distance travelled by both bodies is inversely proportional to coefficient of friction.
$\frac{s_1}{s_2}=\frac{{\mu }_2}{{\mu }_1}=2$