TS EAMCET 18-July-2022 Shift 2 Solved Paper

The given situation is shown below.
Let's assume the block is stationary only till point P .
Slope of point P=tan‌θ (where, θ= angle of repose)
also: ‌‌‌

dy

dx

=‌

d

dx

(‌

x2

20

)=‌

x

10

‌‌‌⋅⋅⋅⋅⋅⋅⋅(i)
We know that, the block will remain stationary only up till angle of repose.
We know, angle of repose θ=tan−1(µs)
⇒θ=tan−1(0.5)
⇒tan‌θ=0.5‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii)
Now, equating (dy∕dx) at P.with tan‌θ from Eqs. (i) and (ii), we get
‌‌

dy

dx

=tan‌θ
⇒‌‌‌

x

10

=0.5⇒x=5
∴‌‌y=‌

x2

20

=‌

25

20

=1.25m