Question 47: Laws of Motion

Question

A body of mass 'm' is launched up on a rough inclined plane making an angle of 30$$^\circ$$ with the horizontal. The coefficient of friction between the body and plane is $${{\sqrt x } \over 5}$$ if the time of ascent is half of the time of descent. The value of x is __________.

Accepted Answer

$${t_a} = {1 \over 2}{t_d}$$
$$\sqrt {{{2s} \over {{a_a}}}}  = {1 \over 2}\sqrt {{{2s} \over {{a_d}}}} $$ ..... (i)
$${a_a} = g\sin 	heta  + \mu g\cos 	heta $$
$$ = {g \over 2} + {{\sqrt 3 } \over 2}\mu g$$
$${a_d} = g\sin 	heta  - \mu g\cos 	heta $$
$$ = {g \over 2} - {{\sqrt 3 } \over 2}\mu g$$
using the above values of a
a
and a
d
and putting in equation (i) we will gate $$\mu  = {{\sqrt 3 } \over 5}$$

Laws of Motion

A body of mass 'm' is launched up on a rough inclined plane making an angle of 30$^\circ with the horizontal. The coefficient of friction between the body and plane is {{\sqrt x } \over 5}$ if the time of ascent is half of the time of descent. The value of x is __________.

Integer / Numeric Answer Type