KCET · Physics · Gravitation
The acceleration due. to gravity becomes \(\left(\frac{g}{2}\right)\) \((g=\) acceleration due to gravity on the surface of the earth) at a height equal to
- A \(4 R\)
- B \(\frac{R}{4}\)
- C \(2 R\)
- D \(\frac{R}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{R}{4}\)
Step-by-step Solution
Detailed explanation
The acceleration due to gravity
\(g=\frac{G M}{R^{2}}\)
At a height \(\mathrm{h}\) above the earth's surface, the acceleration due to gravity is
\(g^{\prime} =\frac{G M}{(R+h)^{2}} \)
\(\frac{g}{g^{\prime}} =\left(\frac{R+h}{R}\right)^{2} \)
\(=\left(1+\frac{h}{R}\right)^{2} \)
\(\frac{g^{\prime}}{g} =\left(1+\frac{h}{R}\right)^{-2} \)
\(=\left(1-\frac{2 h}{R}\right) \)
\(\text {but } \quad \frac{g / 2}{h} =\frac{g}{2} (given) \)
\(\therefore \frac{2 h}{R} =\frac{1}{2} \)
\(h =\frac{R}{4}\)
\(g=\frac{G M}{R^{2}}\)
At a height \(\mathrm{h}\) above the earth's surface, the acceleration due to gravity is
\(g^{\prime} =\frac{G M}{(R+h)^{2}} \)
\(\frac{g}{g^{\prime}} =\left(\frac{R+h}{R}\right)^{2} \)
\(=\left(1+\frac{h}{R}\right)^{2} \)
\(\frac{g^{\prime}}{g} =\left(1+\frac{h}{R}\right)^{-2} \)
\(=\left(1-\frac{2 h}{R}\right) \)
\(\text {but } \quad \frac{g / 2}{h} =\frac{g}{2} (given) \)
\(\therefore \frac{2 h}{R} =\frac{1}{2} \)
\(h =\frac{R}{4}\)
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 \(S_{1}\) having the activity \(\mathrm{A}_{1}\) has twice the number of nuclei as another sample \(S_{2}\) of activity \(A_{2}\). If \(A_{2}=2 A_{1}\), then the ratio of half-life of \(S_{1}\) to the half-life of \(S_{2}\) isKCET 2010 Medium
- A convex lens of focal length \(f\) is placed somewhere in between an object and a screen. The distance between the object and the screen is \(x\). If the numerical value of the magnification produced by the lens is \(m\), then the focal length of the lens isKCET 2022 Hard
- The accurate measurement of emf can be obtained usingKCET 2009 Easy
- A planoconvex lens has a maximum thickness of \(6 \mathrm{~cm}\). When placed on a horizontal table with the curved surface in contact with the table surface, the apparent depth of the bottommost point of the lens is found to be \(4 \mathrm{~cm}\). If the lens is inverted such that the plane face of the lens is in contact with the surface of the table, the apparent depth of the centre of the plane face is found to be \(\left(\frac{17}{4}\right) \mathrm{cm}\). The radius of curvature of the lens isKCET 2011 Hard
- The ratio of volume of \(\mathrm{Al}^{27}\) nucleus to its surfactarea is (Given, \(R_0=1.2 \times 10^{-15} \mathrm{~m}\) )KCET 2024 Easy
- A dipole moment \(p\) and moment of inertia \(I\) is placed in a uniform electric field \(\mathbf{E}\). If it is displaced slightly from its stable equilibrium position, the period of oscillation of dipole isKCET 2020 Easy
More PYQs from KCET
- \(\cos \left[\cot ^{-1}(-\sqrt{3})+\frac{\pi}{6}\right]\) is equal toKCET 2021 Easy
- For which combination of working temperatures of source and sink, the efficiency of Carnot's heat engine is maximum?KCET 2013 Medium
- Orion has monomeric unitKCET 2015 Easy
- If \( \tan ^{-1}\left(x^{2}+y^{2}\right)=\alpha \) then \( \frac{d y}{d x} \) is equal toKCET 2016 Medium
- IUPAC name of \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CCl}\) isKCET 2009 Easy
- In which of the following steps in DNA fingerprinting technique are labelled VNTR probes used?KCET 2018 Hard