Gravitation Question 219
Question: Wires $ [A] $ and $ [B] $ are connected with blocks $ [P] $ and $ [Q] $ , as shown. The ratio of lengths, radii and Young’s modulus of wires $ [A] $ and $ [B] $ are $ [r,,2r] $ and 3r respectively ($ [r] $ is a constant). Find the mass of block $ [P] $ if ratio of increase in their corresponding lengths is $ [\frac{1}{6r^{2}}] $ . The mass of the block $ [Q] $ is 3$ [M] $
Options:
A) $ [M] $
B) $ [3M] $
C) $ [6M] $
D) $ [9M] $
Show Answer
Answer:
Correct Answer: C
Solution:
- $ [\Delta l=\frac{FL}{AY}] $ $ [\frac{\Delta l_{A}}{\Delta l_{B}}=\left( \frac{F_{A}}{F_{B}} \right)\left( \frac{L_{A}}{L_{B}} \right)\left( \frac{A_{B}}{A_{A}} \right)\left( \frac{Y_{B}}{Y_{A}} \right)] $ $ [=\left( \frac{KM}{3M} \right)(r){{\left( \frac{1}{2r} \right)}^{2}}\left( \frac{1}{3r} \right)=\frac{K}{36r^{2}}=\frac{1}{6r^{2}}] $ (given) K=6 Mass of block P=6M
