JEE Mains · Physics · STD 11 - 14. waves and sound
A heavy ball of mass \(M\) is suspended from the ceiling of car by a light string of mass \(m (m << M)\). When the car is at rest, the speed of transverse waves in the string is \(60\, ms^{-1}\). When the car has acceleration \(a\) , the wave-speed increases to \(60.5\, ms^{-1}\). The value of \(a\) , in terms of gravitational acceleration \(g\) is closest to
- A \(\frac{g}{{30}}\)
- B \(\frac{g}{{10}}\)
- C \(\frac{g}{{5}}\)
- D \(\frac{g}{{20}}\)
Answer & Solution
Correct Answer
(C) \(\frac{g}{{5}}\)
Step-by-step Solution
Detailed explanation
\(60=\sqrt{\frac{M g}{\mu}}\) \(60.5=\sqrt{\frac{M\left(g^{2}+a^{2}\right)^{1 / 2}}{\mu}} \Rightarrow \frac{60.5}{60}=\sqrt{\sqrt{\frac{g^{2}+a^{2}}{g^{2}}}}\) \(\left(1+\frac{0.5}{60}\right)^{4}=\frac{g^{2}+a^{2}}{g^{2}}=1+\frac{2}{60}\)…
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