CAT 2003 Slot 2 — QA Question 15
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.)
In the setup of the previous two questions, how is h related to n?
Answer & solution
- A
- B
h = n
- D
h =
The string tied on the cylinder and the cube is of the same length .
Now, we cut the cylinder horizontally such that each turn of the string is now on a separate cylinder. On opening up one of the n cylinders, we get a rectangle whose length is equal to the circumference of the cylinder and whose breadth is equal to h/n. The string will be the diagonal of the rectangle.
Cylinder’s circumference = 2 × π × r = 2 × π × 2/π = 4 units
The string has encircled the cylinder n times, thus the length used in 1 turn
=
From the above figure,
∴ h = n
Hence, option (c).