JEE Mains · Physics · STD 11 - 7. gravitation
Given below are two statements:
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II: The time period of revolution of the satellite is \( T=2\pi\sqrt{\frac{R_{e}}{g}} \) (for satellite very close to the earth surface), where \( R_{e} \) radius of earth and g acceleration due to gravity.
In the light of the above statements, choose the correct answer from the options given below :
- A Both Statement I and Statement II are false
- B Both Statement I and Statement II are true
- C Statement I is true but Statement II is false
- D Statement I is false but Statement II is true
Answer & Solution
Correct Answer
(B) Both Statement I and Statement II are true
Step-by-step Solution
Detailed explanation
\(T =2 \pi \sqrt{\frac{ R ^3}{ GM }}\) \(\because M =\rho \cdot \frac{4}{3} \pi R ^3\) \(\therefore T=2 g p \sqrt{\frac{1}{G \rho \frac{4}{3} \pi}}\) Statement I is correct. And \(\therefore \frac{ GM }{ R ^2}= g\) \(\therefore T =2 \pi \sqrt{\frac{ R }{ g }}\) Statement II is…
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
- Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m . They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process _________ J.JEE Mains 2026 Easy
- A cylinder of mass \(M_c\) and sphere of mass \(M_s\) are placed at points \(A\) and \(B\) of two inclines, respectively (See Figure). If they roll on the incline without sipping such that their accelerations are the same, then the ratio \(\frac{{\sin \,{\theta _c}}}{{\sin \,{\theta _s}}}\) is
JEE Mains 2014 Hard - \(I _{ CM }\) is moment of inertia of a circular disc about an axis \(( CM )\) passing through its center and perpendicular to the plane of disc. \(I _{ AB }\) is it's moment of inertia about an axis \(A B\) perpendicular to plane and parallel to axis \(CM\) at a distance \(\frac{2}{3} R\) from center. Where \(R\) is the radius of the disc. The ratio of \(I _{ AB }\) and \(I _{ CM }\) is \(x: 9\). The value of \(x\) is \(........\)
JEE Mains 2023 Medium - In the isothermal expansion of \(10\,g\) of gas from volume \(V\) to \(2V\) the work done by the gas is \(575\,J\). What is the root mean square speed of the molecules of the gas at that temperature ..... \(m/s\)?JEE Mains 2013 Medium
- The current \(I_{1}\) (in \(A\)) flowing through \(1\; \Omega\) resistor in the following circuit is:
JEE Mains 2020 Medium - A vehicle travels \(4\,km\) with speed of \(3\,km / h\) and another \(4\,km\) with speed of \(5\,km / h\), then its average speed is \(..........km/h\)JEE Mains 2023 Medium
More PYQs from JEE Mains
- The nuclear activity of a radioactive element becomes \(\left(\frac{1}{8}\right)^{\text {th }}\) of its initial value in \(30\, years.\) The half-life of radioactive element is \(....\,years.\)JEE Mains 2021 Medium
- The sum, of the squares of all the roots of the equation \(x^2+|2 x-3|-4=0\), isJEE Mains 2025 Medium
- A perfectly dimagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field \(\overrightarrow{ B }\). Then the field inside the paramagnetic substance is:
JEE Mains 2020 Medium - Let \(y=f(x)\) represent a parabola with focus \(\left(-\frac{1}{2}, 0\right)\) and directrix \(y =-\frac{1}{2}\). Then \(S=\left\{x \in R : \tan ^{-1}\left(\sqrt{f(x)}+\sin ^{-1}(\sqrt{f(x)+1})\right)=\frac{\pi}{2}\right\}:\)JEE Mains 2023 Hard
- For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through \(O\) (the centre of mass) and \(O ^{\prime}(\) corner point \()\) is
JEE Mains 2020 Hard - A hemispherical glass body of radius \(10\, cm\) and refractive index \(1.5\) is silvered on its curved surface. A small air bubble is \(6\, cm\) below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen
JEE Mains 2016 Hard