MHT CET · Physics · Gravitation
Two satellites 'A' and 'B' are revolving with critical velocities ' \(\mathrm{v}_{\mathrm{A}}\) ' and ' \(\mathrm{v}_{\mathrm{B}}\) ' around the earth, in circular orbits of radii ' \(\mathrm{R}\) ' and ' \(2 \mathrm{R}^{\prime}\), respectively. The ratio \(\frac{\mathrm{V}_{\mathrm{A}}^{\prime}}{\mathrm{V}_{\mathrm{B}}}\) is
- A \(2: 1\)
- B \(\sqrt{2}: 1\)
- C \(1: 2\)
- D \(1: \sqrt{2}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{2}: 1\)
Step-by-step Solution
Detailed explanation
Critical velocity of the satellite is given by
\( \begin{aligned} \mathrm{V} &=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}} \\ \therefore \frac{\mathrm{V}_{\mathrm{A}}}{\mathrm{V}_{\mathrm{B}}} &=\sqrt{\frac{2 \mathrm{R}}{\mathrm{R}}}=\sqrt{2} \end{aligned} \)
\( \begin{aligned} \mathrm{V} &=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}} \\ \therefore \frac{\mathrm{V}_{\mathrm{A}}}{\mathrm{V}_{\mathrm{B}}} &=\sqrt{\frac{2 \mathrm{R}}{\mathrm{R}}}=\sqrt{2} \end{aligned} \)
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 step-down transformer has turns ratio 20: 1 . If \(8 \mathrm{~V}\) is applied across 0.4 ohm secondary coil, then the primary current willMHT CET 2021 Medium
- From a metallic surface photoelectric emission is observed for frequencies \(v_1\) and \(v_2\left(v_1>v_2\right)\) of the incident light. The maximum values of the kinetic energy of the photoelectrons emitted in the two cases are in the ratio \(1: \mathrm{x}\). Hence the threshold frequency of the metallic surface isMHT CET 2023 Medium
- A uniform metal wire has length ' \(L\) ', mass ' \(M\) ' and cross-sectional area ' \(A\) '. It is under tension ' \(T\) ' and ' \(V\) ' is the speed of transverse wave along the wire. The density of the wireMHT CET 2022 Medium
- Four identical uniform solid spheres each of same mass ' \(M\) ' and radius ' \(R\) ' are placed touching each other as shown in figure, with centres \(A, B, C, D . I_A, I_B, I_C\) and \(I_D\) are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane. The difference in \(\mathrm{I}_{\mathrm{A}}\), and \(\mathrm{I}_{\mathrm{B}}\) is
MHT CET 2023 Hard - A mass attached to a spring performs S.H.M. whose displacement is \(\mathrm{x}=3 \times 10^{-3} \cos 2 \pi \mathrm{t}\) metre. The time taken to obtain maximum speed for the first time isMHT CET 2025 Medium
- Liquid drops are falling slowly one by one from vertical glass tube. The relation between the weight of a drop ' \(w\) ', the surface tension ' \(T\) ' and the radius ' \(r\) ' of the bore of the tube is (Angle of contact is zero)MHT CET 2024 Easy
More PYQs from MHT CET
- The pdf of a random variable X is 0 otherwise. TheMHT CET 2019 Hard
- What is the number of chiral carbon atoms present in 2-chloro-3,4-dimethylhexane?MHT CET 2024 Medium
- DPD of a cell can be expressed as __________.MHT CET 2020 Hard
- A coil of ' \(n\) ' turns and radius ' \(R\) ' carries a current 'I'. It is unwound and rewound to make a new coil of radius \(\frac{R}{3}\) and the same current is passed through it. The ratio of the magnetic moment of the new coil to that of the original coil isMHT CET 2024 Easy
- Calculate the density of metal having molar mass \(210 \mathrm{~g} \mathrm{~mol}^{-1}\) that forms simple cubic unit cell. \(\left(\mathrm{a}^3 \cdot \mathrm{N}_{\mathrm{A}}=21.5 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right)\)MHT CET 2023 Medium
- What is the molar conductivity at infinite dilution of \(\mathrm{CaCl}_{2}\), if the molar conductivity of \(\mathrm{Ca}^{2+}\) ion and \(\mathrm{Cl}^{-}\) ion at infinite dilution is 119 and \(71 \Omega^{-1} \mathrm{~cm}^{2}\) \(\mathrm{mol}^{-1}\)MHT CET 2020 Easy