WBJEE · Physics · Laws of Motion
If a string, suspended from the ceilling is given a downward force \(F_1\), its length becomes \(L_1\), Its length is \(L_2\), if the downward force is \(\mathrm{F}_2\). What is its actual length?
- A \(\frac{L_1+L_2}{2}\)
- B \(\sqrt{L_1 L_2}\)
- C \(\frac{\mathrm{F}_2 \mathrm{~L}_1+\mathrm{F}_1 \mathrm{~L}_2}{\mathrm{~F}_2+\mathrm{F}_1}\)
- D \(\frac{\mathrm{F}_2 \mathrm{~L}_1-\mathrm{F}_1 \mathrm{~L}_2}{\mathrm{~F}_2-\mathrm{F}_1}\)
Answer & Solution
Correct Answer
(D) \(\frac{\mathrm{F}_2 \mathrm{~L}_1-\mathrm{F}_1 \mathrm{~L}_2}{\mathrm{~F}_2-\mathrm{F}_1}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} &\left(L_1-L\right)=\frac{F_1 L}{A y} ; L_2-L=\frac{F_2 L}{A y} \\ \Rightarrow & \frac{L_1-L}{L_2-L}=\frac{F_1}{F_2} \Rightarrow F_2 L_1-F_2 L=F_1 L_2-F_1 L \Rightarrow L=\frac{F_2 L_1-F_1 L_2}{F_2-F_1} \end{aligned}\)
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