SATHEE: Gravitation Question 219

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 $[r,, 2 r]$ and 3r respectively ( $[r]$ is a constant). Find the mass of block $[P]$ if ratio of increase in their corresponding lengths is $[\frac{1}{6 r^{2}}]$ . The mass of the block $[Q]$ is 3 $[M]$

Options:

A) $[M]$

B) $[3 M]$

C) $[6 M]$

D) $[9 M]$

Show Answer

Answer:

Correct Answer: C

Solution:

$[Δ l = \frac{F L}{A Y}]$ $[\frac{Δ l_{A}}{Δ l_{B}} = (\frac{F_{A}}{F_{B}}) (\frac{L_{A}}{L_{B}}) (\frac{A_{B}}{A_{A}}) (\frac{Y_{B}}{Y_{A}})]$ $[= (\frac{K M}{3 M}) (r) {(\frac{1}{2 r})}^{2} (\frac{1}{3 r}) = \frac{K}{36 r^{2}} = \frac{1}{6 r^{2}}]$ (given) K=6 Mass of block P=6M

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Gravitation Question 219

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