MHT CET · Physics · Oscillations
The length of the seconds pendulum is decreased by \(0.3 \mathrm{~cm}\) when it is shifted from
place A to place B. If the acceleration due to gravity at place \(\mathrm{A}\) is \(981 \mathrm{~cm} / \mathrm{s}^{2}\), the
acceleration due to gravity at place \(\mathrm{B}\) is \(\left(\right.\) Take \(\pi^{2}=10\) )
- A \(975 \mathrm{Cm} / \mathrm{S}^{2}\)
- B \(978 \mathrm{~cm} / \mathrm{s}^{2}\)
- C \(984 \mathrm{~cm} / \mathrm{s}^{2}\)
- D \(981 \mathrm{Cm} / \mathrm{s}^{2}\)
Answer & Solution
Correct Answer
(B) \(978 \mathrm{~cm} / \mathrm{s}^{2}\)
Step-by-step Solution
Detailed explanation
For seconds pendulum \(\mathrm{T}=26\)
\(T=2 \pi \sqrt{\frac{1}{g}} \quad \therefore \quad 2=2 \pi \sqrt{\frac{\ell}{g}}\)
of \(1=\pi \sqrt{\frac{l}{g}}\)
gquaring: \(1=\pi^{2} \frac{\ell}{g}\)
\(t=\frac{9}{\pi^{2}}=\frac{981}{10}=98.1 \mathrm{~cm}\)
At place B, \(\ell^{\prime}=98.1-0.3=97.8 \mathrm{~cm}\)
Again, \(2=2 \pi \sqrt{\frac{\ell^{\prime}}{\mathrm{g}^{\prime}}}\)
\(1=\pi^{2} \frac{\mathscr{L}}{\mathrm{g}^{\prime}}\)
\(\therefore g^{\prime}=\pi^{2} \ell^{\prime}=10 \times 97.8=978 \mathrm{~cm} / \mathrm{s}^{2}\)
\(T=2 \pi \sqrt{\frac{1}{g}} \quad \therefore \quad 2=2 \pi \sqrt{\frac{\ell}{g}}\)
of \(1=\pi \sqrt{\frac{l}{g}}\)
gquaring: \(1=\pi^{2} \frac{\ell}{g}\)
\(t=\frac{9}{\pi^{2}}=\frac{981}{10}=98.1 \mathrm{~cm}\)
At place B, \(\ell^{\prime}=98.1-0.3=97.8 \mathrm{~cm}\)
Again, \(2=2 \pi \sqrt{\frac{\ell^{\prime}}{\mathrm{g}^{\prime}}}\)
\(1=\pi^{2} \frac{\mathscr{L}}{\mathrm{g}^{\prime}}\)
\(\therefore g^{\prime}=\pi^{2} \ell^{\prime}=10 \times 97.8=978 \mathrm{~cm} / \mathrm{s}^{2}\)
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
- A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will beMHT CET 2023 Medium
- The magnetic field ( \(B\) ) inside a long solenoid having \(n\) turns per unit length and carrying current \(I\) when iron core is kept in it is ( \(\mu_0=\) permeability of vacuum, \(\chi=\) magnetic susceptibility)MHT CET 2016 Medium
- In a circuit, the current lags behind the voltage by a phase difference of \(\pi / 2\), the circuit will contain which of the following ?MHT CET 2007 Medium
- An n-p-n transistor can be considered to be equivalent to two diodes connected. The correct figure out of the following is
(a)
(b)
(c)
(d)
MHT CET 2024 Easy - What will be the self inductance of a coil of 100 turns if a current of 5 A produces a magnetic flux \(5 \times 10^{-5} \mathrm{~Wb}\) ?MHT CET 2011 Easy
- For any two vectors \(\vec{A}\) and \(\vec{B}\) if \(\vec{A} \cdot \vec{B}=|\vec{A} \times \vec{B}|\), the magnitude of
\((\vec{A}+\vec{B})\) is \(\left(\tan \frac{\pi}{4}=1, \cos \frac{\pi}{4}=\frac{1}{\sqrt{2}}\right)\)MHT CET 2020 Medium
More PYQs from MHT CET
- A mine is located at depth \(\frac{\mathrm{R}}{3}\) below earth's surface. The acceleration due to gravity at that depth in mine is ( \(\mathrm{R}=\) radius of earth, \(\mathrm{g}\) = acceleration due to gravity)MHT CET 2023 Medium
- Bacteria increases at the rate proportional to the number of bacteria present. If the original number N doubles in 4 hours, then the number of bacteria will be \(4 \mathrm{~N}\) inMHT CET 2020 Easy
- If the amplitude of linear S.H.M. is decreased thenMHT CET 2021 Medium
- The objective function subject to has minimum value at the pointMHT CET 2017 Hard
- Tert-butyl methyl ether on treatment with hydrogen iodide in cold givesMHT CET 2017 Medium
- When a capacitor is connected in series LR circuit, the alternating current flowing in the circuitMHT CET 2024 Easy