CAT 2003 Slot 2 — QA Question 13

Basics of Mensuration/PrismEasy

Passage / Data

Answer the following question based on the information given below.

Consider a cylinder of height h cms and radius r = 2/π cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of n turns (in other words, the string’s length is the minimum length required to wind n turns.)

What is the vertical spacing in cms between two consecutive turns?

Answer & solution

Correct answer: h n

$\frac{h}{n}$
B
$\frac{h}{\sqrt{n}}$
C
$\frac{h}{n^{2}}$
D
Cannot be determined with given information

Solution

The equivalent spacing between two consecutive turns = $\frac{H e i g h t o f t h e c y l i n d e r}{N u m b e r o f t u r n s} = \frac{h}{n}$

Hence, option (a).

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