MHT CET · Physics · Gravitation
The acceleration due to gravity on moon is \(\frac{1^{\text {th }}}{6}\) times the acceleration due to gravity on earth. If the ratio of the density of earth ' \(e_e\) ' to the density of moon ' \(e_m\) ' is \(\frac{5}{3}\) then the radius of moon ' \(R_m\) ' in terms of the radius of earth ' \(R_e\) ' is
- A \(\left(\frac{3}{18}\right) \mathrm{R}_{\mathrm{e}}\)
- B \(\left(\frac{1}{2 \sqrt{3}}\right) \mathrm{R}_{\mathrm{e}}\)
- C \(\left(\frac{5}{18}\right) \mathrm{R}_{\mathrm{e}}\)
- D \(\left(\frac{7}{6}\right) \mathrm{R}_{\mathrm{e}}\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{5}{18}\right) \mathrm{R}_{\mathrm{e}}\)
Step-by-step Solution
Detailed explanation
We know \(g=\frac{\mathrm{GM}}{\mathrm{R}^2}\)
And the relation between mass and density of the planet is given by
\(\begin{aligned} & M=\rho\left(\frac{4}{3} \pi R^3\right) \\ & \therefore g=\left(\frac{4 \pi G}{3}\right) \rho R=K \rho R\end{aligned}\)
Given, \(\mathrm{g}_{\mathrm{m}}=\frac{1}{6} \mathrm{~g}_{\mathrm{e}}\) and \(\mathrm{e}_{\mathrm{m}}=\frac{3}{5} \mathrm{e}_{\mathrm{e}}\)
\(\begin{aligned} & \Rightarrow \frac{g_m}{g_e}=\frac{e_m R_m}{e_e R_e}=\frac{1}{6} \\ & \Rightarrow \frac{3 R_m}{5 R_e}=\frac{1}{6} \\ & \Rightarrow R_m=\frac{5}{18} R_e\end{aligned}\)
And the relation between mass and density of the planet is given by
\(\begin{aligned} & M=\rho\left(\frac{4}{3} \pi R^3\right) \\ & \therefore g=\left(\frac{4 \pi G}{3}\right) \rho R=K \rho R\end{aligned}\)
Given, \(\mathrm{g}_{\mathrm{m}}=\frac{1}{6} \mathrm{~g}_{\mathrm{e}}\) and \(\mathrm{e}_{\mathrm{m}}=\frac{3}{5} \mathrm{e}_{\mathrm{e}}\)
\(\begin{aligned} & \Rightarrow \frac{g_m}{g_e}=\frac{e_m R_m}{e_e R_e}=\frac{1}{6} \\ & \Rightarrow \frac{3 R_m}{5 R_e}=\frac{1}{6} \\ & \Rightarrow R_m=\frac{5}{18} R_e\end{aligned}\)
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
- Force is applied to a body of mass 3 kg at rest on a frictionless horizontal surface as shown in the force against time (F - t) graph. The speed of the body after 1 s is
MHT CET 2025 Medium - If a capillary tube of radius \(1 \mathrm{~mm}\) is immersed in water, the mass of water rising in the capillary tube is \(\mathrm{m}\). If the radius of the capillary tube is doubled, then the mass of water that rises in the same capillary tube will beMHT CET 2022 Medium
- A small ball of mass \(M\), radius \(R\) and density \(\rho\) moves with terminal velocity through a container filled with glycerine of density \(\sigma\). The viscous force acting on the ball is ( \(g=\) gravitational acceleration)MHT CET 2022 Medium
- In series LCR circuit, resistance is \(18 \Omega\) and impedance is \(33 \Omega\). An r.m.s. voltage of
\(220 \mathrm{~V}\) is applied across the circuit. The true power consumed in a.c. circuit isMHT CET 2020 Medium - If ' \(\lambda_1\) ' and ' \(\lambda_2\) ' are the wavelengths of the first line of the Lyman and Paschen series respectively, then \(\lambda_2: \lambda_1\) isMHT CET 2024 Easy
- 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 \(\frac{\mathrm{V}_{\mathrm{A}}^{\prime}}{\mathrm{V}_{\mathrm{B}}}\) isMHT CET 2020 Easy
More PYQs from MHT CET
- The solution set of the inequalities \(4 x+3 y \leq 60, y \geq 2 x, x \geq 3, x, y \geq 0\) is represented by region
MHT CET 2023 Hard - Match the enzyme involved in Krebs cycle given in column-I with the reactions they catalyse given in column-II. Choose the correct option.
Column I Column II i. Isocitrate dehydrogenase a. Citrate → Cisaconitate ii. Fumarase b. Succinate → Fumarate iii. Aconitase c. Fumarate → Malate Iv. Succinate dehydrogenase d. Isocitrate → Oxalosuccinic acid MHT CET 2023 Easy - If \(\mathrm{O}(0,0), \mathrm{A}(1,2)\) and \(\mathrm{B}(3,4)\) are the vertices of triangle OAB , then the joint equation of the altitude and median drawn from O isMHT CET 2024 Hard
- Which from following is a copolymer ?MHT CET 2024 Easy
- Given below are two statements.
Statement I - During respiration the respiratory substrate directly unite with oxygen.
Statement II - The primary process of respiration consists of removal of hydrogen from the respiratory substrate.
In the light of above statements, Select the correct option given below:MHT CET 2025 Hard - A mass attached to one end of a string crosses topmost point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( gravitational acceleration)MHT CET 2017 Easy