Question

$\footnotesize{\underline{\textsf{\textbf{\red{Q\;U\;E\;S\;T\;I\;O\;N\;\;\;:-}}}}}$
When a body slides down from rest along a smooth inclined plane making an angle of 45° with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the co-efficient of friction between the body and the rough plane.
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Answer 1

Here in this case for the question 1 ,

When the two objects of velocities say v and v ' respectively are moving in the opposite direction or towards each other.

Relative velocity of the two bodies in this case is :

v- (-v') = v + v'.

In the given question,

Relative velocity=8+4 =12 m/s

Since,

Speed=Distance / Time

Time = distance/speed,

= 1200 /12=100 sec=1 min 40 seconds

Thus, they will take 1 min 40 seconds hours to reach the common point.

Answer 2

Answer:

$\sf \: coefficient \: of \: friction \:between\:the\:body\:and\\\sf\:the\:rough\:plane\: : \: \: \\ \sf \mu = 1 - \frac{1}{ {p}^{2} }$

Explanation:

see the attachment please