AP EAMCET · PHYSICS · Gravitation
An infinite number of objects each 1 kg mass are placed on the x -axis on both sides of \(\mathrm{x}=0\) at \(\pm 1 \mathrm{~m}, \pm 2 \mathrm{~m}, \pm 4 \mathrm{~m}, \pm 8 \mathrm{~m} \ldots\) and so on. The magnitude of the resultant gravitational potential (in SI units) at \(x=0\) is
(G - Universal gravitational constant)
- A \(-G\)
- B \(-2 \mathrm{G}\)
- C \(-3 \mathrm{G}\)
- D \(-4 \mathrm{G}\)
Answer & Solution
Correct Answer
(D) \(-4 \mathrm{G}\)
Step-by-step Solution
Detailed explanation
\(V = \sum_{n=0}^{\infty} \left( -\frac{Gm}{2^n} \right) + \sum_{n=0}^{\infty} \left( -\frac{Gm}{2^n} \right)\) \(V = -2Gm \sum_{n=0}^{\infty} \left(\frac{1}{2}\right)^n\) \(V = -2G(1) \left(\frac{1}{1 - \frac{1}{2}}\right)\) \(V = -2G(2)\) \(V = -4G\)
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 bullet of mass \(10 \mathrm{~g}\) pierces through a plate \(A\) of mass \(500 \mathrm{~g}\) and then gets embedded into a second plate \(B\) of mass \(1.49 \mathrm{~kg}\) as shown in the figure. Initially, the two plates \(A\) and \(B\) are at rest and move with same velocity after collision. The percentage loss in the initial kinetic energy of the bullet, when it is between the plates \(A\) and \(B\) is _______
(Neglect any loss of material of the plates during the collision)
[QUESTION]
AP EAMCET 2018 Hard - An air column in a tube \(32 \mathrm{~cm}\) long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length \(66 \mathrm{~cm}\) is in resonance with
another tuning fork. When these two tuning forks are sounded together, they produce 8 beats per second. Then the frequencies of the two tuning forks are, (Consider fundamental frequencies only)AP EAMCET 2013 Hard - A ball of mass \(1 \mathrm{~g}\) having a charge of \(20 \mu \mathrm{C}\) is tied to one end of a string of length \(0.9 \mathrm{~m}\) can rotate in a vertical plane in a uniform electric field \(100 \mathrm{NC}^{-1}\) directed upwards. The minimum horizontal velocity that must be given to the ball at the lowest position so
that it completes the vertical circle is (Let, \(\mathrm{g}=10 \mathrm{~ms}^{-2}\))AP EAMCET 2019 Hard - A spherical ball of volume \(2000 \mathrm{~cm}^3\) is subjected to a hydraulic pressure of \(15 \mathrm{~atm}\). If the change in volume is \(5 \times 10^{-2} \mathrm{~cm}^3\), the bulk modules of the material of the spherical ball is
\(\left(1 \mathrm{~atm}=10^5 \mathrm{Nm}^{-2}\right)\)AP EAMCET 2023 Easy - When a \(0.75 \mu \mathrm{F}\) capacitor is charged to a voltage of \(20 \mathrm{~V}\), then the magnitude of charge on each plate isAP EAMCET 2021 Easy
- When 100 J of heat is supplied to a gas, the increase in the internal energy of the gas is 60 J . Then the gas is/canAP EAMCET 2024 Easy
More PYQs from AP EAMCET
- Two balls are drawn from an urn containing 7 white, 6 red and 8 black balls one after the other without replacement. Then the probability that atleast one of them is white, isAP EAMCET 2018 Easy
- Which of the following salts form hydrates?
\(\begin{array}{lcccc}\mathrm{CaCl}_2 & \mathrm{NaCl} & \mathrm{LiCl} & \mathrm{BaCl}_2 & \mathrm{KCl} \\ \text { I } & \text { II } & \text { III } & \text { IV } & \text { V }\end{array}\)AP EAMCET 2022 Easy - Let \(\mathrm{X}\) - axis be the transverse axis and \(\mathrm{Y}\)-axis be the conjugate axis of a hyperbola \(\mathrm{H}\). Let \(\mathrm{x}^2+\mathrm{y}^2=16\) be the director circle of \(\mathrm{H}\). If the perpendicular distance from the centre of \(\mathrm{H}\) to its latus rectum is \(\sqrt{34}\) then \(\mathrm{a}+\mathrm{b}=\)AP EAMCET 2023 Easy
- If \(-\frac{\pi}{4} < x < \frac{\pi}{4}\), then the general solution of the differential equation \(\cos ^2 x \cdot \frac{d y}{d x}-(\tan 2 x) y=\cos ^4 x\) isAP EAMCET 2018 Easy
- Two charges each of charge \(+10 \mu C\) are kept on \(Y\)-axis at \(y=-a\) and \(y=+a\), respectively. Another point charge \(-20 \mu C\) is placed at the origin and given a small displacement \(x(x< < a)\) along \(X\)-axis. The force acting on the point charge is
\(\left(x \text { and } a \text { are in metres, } \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~N}-\mathrm{m}^2 \mathrm{C}^{-2}\right)\)AP EAMCET 2016 Easy - In the given reaction sequence, conversion of X to Y is an example of
AP EAMCET 2025 Easy