Question

An object is placed on the surface of a smooth inclined plane of inclination $\theta$it takes time $t_1$ to reach the bottom if the some object is allowed to slide down a rough inclined plane of inclination $\theta$ it takes time $t_2$. find the relation between $t_1$ and $t_2$

Answer 1

$mg\sin \theta =ma$

$\Rightarrow a=g\sin \theta$

$N=mg\cos \theta$

$f_s=\mu mg\cos \theta$

$mg\sin \theta -\mu mg\cos \theta -m{a}^{\prime }$

$(g\sin \theta -\mu \cos \theta )=a^{\prime }$

$sa{a}^{\prime }<a$

Hence $t_1<t_2$