MHT CET · Physics · Oscillations
A body of mass \(64 \mathrm{~g}\) is made to oscillate turn by turn on two different springs A and B. Spring \(\mathrm{A}\) and \(\mathrm{B}\) has force constant \(4 \frac{\mathrm{N}}{\mathrm{m}}\) and \(16 \frac{\mathrm{N}}{\mathrm{m}}\) respectively. If \(\mathrm{T}_{1}\) and \(\mathrm{T}_{2}\) are period of oscillations of springs \(\mathrm{A}\) and \(\mathrm{B}\) respectively then \(\frac{\mathrm{T}_{1}+\mathrm{T}_{2}}{\mathrm{~T}_{1}-\mathrm{T}_{2}}\) will be
- A \(1: 3\)
- B \(3: 1\)
- C \(1: 2\)
- D \(2: 1\)
Answer & Solution
Correct Answer
(B) \(3: 1\)
Step-by-step Solution
Detailed explanation
(A)
\(T=2 \pi \sqrt{\frac{m}{k}} \quad \therefore \frac{T_{1}}{T_{2}}=\sqrt{\frac{k_{2}}{k_{1}}}=\sqrt{\frac{16}{4}}=\frac{2}{1}\)
\(=\frac{T_{1}+T_{2}}{T_{1}-T_{2}}\)
\(T=2 \pi \sqrt{\frac{m}{k}} \quad \therefore \frac{T_{1}}{T_{2}}=\sqrt{\frac{k_{2}}{k_{1}}}=\sqrt{\frac{16}{4}}=\frac{2}{1}\)
\(=\frac{T_{1}+T_{2}}{T_{1}-T_{2}}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- The temperature of a gas is measure ofMHT CET 2023 Easy
- The length of potentiometer wire is \(4 \mathrm{~m}\) and is connected in series with an
accumulator. The e.m.f. (Unknown) of a cell balances against \(1 \cdot 5 \mathrm{~m}\) length of wire.
If the length of potentiometer wire is doubled, then the new balancing length of
wire will beMHT CET 2020 Easy - If the length of the oscillating simple pendulum is made \(\frac{1}{3}\) times the original keeping amplitude same then increase in its total energy at a place will beMHT CET 2025 Medium
- The potential energy of a molecule on the surface of a liquid compared to one inside the liquid isMHT CET 2008 Easy
- The potential difference \(\left(\mathrm{V}_{\mathrm{A}}-\mathrm{V}_{\mathrm{B}}\right)\) between the points ' A ' and ' B ' in the given part of the circuit is
MHT CET 2024 Easy - A prism having refractive index \(\sqrt{2}\) and refracting angle \(30^{\circ}\) has one of the
refracting surfaces silvered. The beam of light incident on the other refracting
surface will retrace its path, if angle of incidence is \(\left[\sin \frac{\pi}{6}=0 \cdot 5\right]\)MHT CET 2020 Medium
More PYQs from MHT CET
- Calculate the oxidation number of Cr in \(\mathrm{CrO}_4^{2-}\) ion and \(\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7\) respectively.MHT CET 2024 Medium
- If the probability density function of a continuous random variable is \(f(x)=\frac{x^{3}}{3}\) if \(-1 < x < 2\)
\(=0\), otherwise,
then the cumulative distribution function of \(X\) isMHT CET 2020 Medium - The dissociation constant of a weak monobasic acid is \(3.2 \times 10^{-4}\). Calculate the degree of dissociation in its 0.04 M solution.MHT CET 2024 Medium
- The equation of the circle whose entre lies on the line \(x-4 y=1\) and which passes through the points \((3,7)\) and \((5,5)\) isMHT CET 2021 Medium
- If \(y=\sin ^2\left(\cot ^{-1} \sqrt{\frac{1+x}{1-x}}\right)\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) has the valueMHT CET 2024 Medium
- Which from following species acts as base, according to Bronsted-Lowry theory? \(\mathrm{HCl}+\mathrm{NH}_3 \rightleftharpoons \mathrm{NH}_{4(\mathrm{aq})}^{+}+\mathrm{Cl}_{(\mathrm{aq})}^{-}\)MHT CET 2024 Hard