Statement-1 (A): If a race track is in the form of a ring whose o… - Vidyadip

MCQ

Statement-1 (A): If a race track is in the form of a ring whose outer and inner radii differ by 10 m then the absolute ratio of the area of the track and the sum of the two boundries is $10: 3$.
Statement-2 (R): If a race track is in the form of a ring whose outer and inner radii are $R$ and $r$, then the area of the track and the sum of its two boundries are in the absolute ratio $(R-r): 2$.

A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
C
Statement-1 is True, Statement-2 is False.
✓
Statement-1 is False, Statement- 2 is True.

✓

Answer

Correct option: D.

Statement-1 is False, Statement- 2 is True.

(D)
Let $A$ denote the area of the track and $C$ be the sum of lengths of two boundries. Then,
$
A=\pi R^2-\pi r^2=\pi\left(R^2+r^2\right)=\pi(R+r)(R-r) \text { and, } C=2 \pi R+2 \pi r=2 \pi(R+r)
$
Then, $ \qquad A: C=\pi(R+r)(R-r): 2 \pi(R+r)=(R-r): 2 \qquad\ldots (i) $
So, statement- 2 is true. Replacing $R-r$ by 10 in (i), we obtain: $A: C=10: 2=5: 1$ So, statement-1 is not true. Hence, option (d) is correct.

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