MHT CET · Physics · Oscillations
The force constant of an oscillating simple pendulum is
- A Independent of mass of the bob as well as length of the pendulum
- B Inversely proportional to mass of the bob and length of the pendulum
- C Directly proportional to the mass of the bob
- D Directly proportional to length of the bob
Answer & Solution
Correct Answer
(C) Directly proportional to the mass of the bob
Step-by-step Solution
Detailed explanation
For a simple pendulum, restoring torque equates the
\(\begin{aligned}
& \tau=-m g L \sin \theta=I \alpha \\
& \Rightarrow \alpha=-\frac{m g L}{m L^2} \sin \theta \approx-\frac{g}{L} \theta \\
& \alpha \approx-\left(\frac{g}{L}\right) \theta \Rightarrow \alpha=-\omega^2 \theta=-\left(\frac{g}{L}\right) \theta
\end{aligned}\)
Force constant of an oscillating simple pendulum is given by \(k=m \omega^2\) \(k \propto m\) and \(k \propto \omega^2=\left(\frac{g}{L}\right)\)
Therefore, force constant of an oscillating simple pendulum is directly proportional to the mass of the bob.
\(\begin{aligned}
& \tau=-m g L \sin \theta=I \alpha \\
& \Rightarrow \alpha=-\frac{m g L}{m L^2} \sin \theta \approx-\frac{g}{L} \theta \\
& \alpha \approx-\left(\frac{g}{L}\right) \theta \Rightarrow \alpha=-\omega^2 \theta=-\left(\frac{g}{L}\right) \theta
\end{aligned}\)
Force constant of an oscillating simple pendulum is given by \(k=m \omega^2\) \(k \propto m\) and \(k \propto \omega^2=\left(\frac{g}{L}\right)\)
Therefore, force constant of an oscillating simple pendulum is directly proportional to the mass of the bob.
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
- When a resistance of \(100 \Omega\) is connected in series with a galvanometer of resistance \(G\), its range is V . To double its range a resistance of \(1000 \Omega\) is connected in series. The value of \(G\) isMHT CET 2024 Easy
- The ratio of the specific heats \(\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma\), in terms of degrees of freedom ( n ) isMHT CET 2024 Medium
- A bomb is dropped by an aero plane flying horizontally with a velocity \(200 \mathrm{~km} / \mathrm{hr}\) and at a height of \(980 \mathrm{~m}\). At the time of dropping a bomb, the distance of the aero plane from the target on the ground to hit directly is \(\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right.\) )MHT CET 2021 Easy
- A simple pendulum oscillates with an angular amplitude \(\theta\). If the maximum tension in the string is 4 times the minimum tension then the value of \(\theta\) isMHT CET 2025 Hard
- In light emitting diode (LED), light is given out due toMHT CET 2020 Easy
- Four point charges each \(+q\) is placed on the circumference of a circle of diameter 2 d in such a way that they form a square. The potential at the centre is proportional toMHT CET 2024 Medium
More PYQs from MHT CET
- Which among the following decreasing order of boiling points is correct for amines?MHT CET 2020 Medium
- A beam of light is incident on a glass plate at an angle of \(60^{\circ}\). The reflected ray is polarized. If angle of incidence is \(45^{\circ}\) then angle of refraction isMHT CET 2023 Hard
- Which among the following is a double ring containing nitrogen base present in nucleic acids?MHT CET 2021 Hard
- The value of \(\int \mathrm{e}^x\left(\frac{1-\sin x}{1-\cos x}\right) \mathrm{dx}\) is equal toMHT CET 2024 Easy
- \(\lim _{x \rightarrow \infty} x^3\left\{\sqrt{x^2+\sqrt{1+x^4}}-x \sqrt{2}\right\}=\)MHT CET 2023 Easy
- If is the integration factor of the linear differential equation then isMHT CET 2016 Easy