AMU Engineering 2018 solved paper Solved Paper

Figure represents situation, as given in question, Rk When body slides on smooth inclined plane at a distance ' d′, then time taken by the body is t,
d=0+

1

2

g‌sin‌45°‌t2
d=

gt2

2√2

.......(i)
When body slides on rough incline plane, then time taken by body to slide same distance ' d ' is nt,
Acceleration of body on rough plane, a′=g‌sin‌45°−µg‌cos‌45°
=

g

√2

−

µg

√2

=

g

√2

(1−µ)
By equation of motion,
∴ d=0+

1

2

a′(nt)2
d=

1

2

.

g

√2

(1−µ)n2t2 ......(ii)
From Eqs. (i) and Eqs. (ii), we get

gt2

2√2

=

g

2√2

(1−µ)n2t2
1=(1−µ)n2
⇒µ=1−

1

n2