Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
The resistance of a wire is directly proportional to its length and inversely proportional to the square of its radius. Two wires of the same material have the same resistance and their radii are in the ratio of 9 : 8. If the length of the first wire is 162 cm, find the length of the other wire. 1 l kl
Answer
Answer (as printed):
Explanation
Clearly, we have : R ∝ l and R ∝ 2 ⇒ R ∝ 2 ⇒ R = 2 , where k is a constant. r r r Let the radii of the two wires be 9x and 8x and their lengths be l1 and l2 respectively. k l1 k l2 l l l 162 Then, 2 = 2 ⇒ 12 = 22 ⇒ 2 = =2 (9 x ) (8 x ) 81x 64 x 64 81 ⇒ l2 = (64 × 2) cm = 128 cm Hence, length of the other wire = 128 cm.
Explanation as extracted from the printed page; notation may be imperfect.