GATE (GA) Textile 2017 Question Paper Solution | GATE/2017/GA/58

Question 58 (General Aptitude)

A right-angled cone (with base radius 5 cm and height 12 cm) as shown in the figure below, is rolled on the ground keeping the point P fixed until the point Q (at the base of the cone, as shown) touches the ground again.
By what angle (in radius) about P does the cone travel ?

Gate Textile Solution 2017
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Given in the figure-
Inclined height(slant height,l)=\sqrt(r^2+h^2)
l=13 cm

Here, As cone is rolling over circumference 360 deg.
Let the cone angle=\theta
2\pi\times r=l\times \theta
2\pi\times5=13\times \theta
\theta=\frac{10\pi}{13} (Ans)

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