Question:
Two planets A and B are orbiting around the sun. The distances of the two planets A and B from the sun are \(r_A\) and \(r_B\) respectively. Also \(r_B = 225\,r_A\). If the orbital speed of the planet A is 'V' then the orbital speed of planet B will be
Two planets A and B are orbiting around the sun. The distances of the two planets A and B from the sun are \(r_A\) and \(r_B\) respectively. Also \(r_B = 225\,r_A\). If the orbital speed of the planet A is 'V' then the orbital speed of planet B will be
Show Hint
Orbital speed around the sun is inversely proportional to the square root of the orbit radius.
Updated On: Oct 1, 2026
- \(\frac{V}{3}\)
- \(\frac{V}{5}\)
- \(\frac{V}{15}\)
- \(\sqrt{15}\,V\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
For a planet in a circular orbit, gravity supplies the centripetal force: \(\frac{GMm}{r^2} = \frac{mv^2}{r}\), so \(v = \sqrt{\frac{GM}{r}}\).
Step 2: Ratio:
\[ \frac{v_A}{v_B} = \sqrt{\frac{r_B}{r_A}} = \sqrt{100} = 10 \]
The planet closer to the sun moves faster, which is consistent with the ratio being greater than 1.
Final Answer:
The ratio of the speeds is 10, option (C). \[ \boxed{10} \]
For a planet in a circular orbit, gravity supplies the centripetal force: \(\frac{GMm}{r^2} = \frac{mv^2}{r}\), so \(v = \sqrt{\frac{GM}{r}}\).
Step 2: Ratio:
\[ \frac{v_A}{v_B} = \sqrt{\frac{r_B}{r_A}} = \sqrt{100} = 10 \]
The planet closer to the sun moves faster, which is consistent with the ratio being greater than 1.
Final Answer:
The ratio of the speeds is 10, option (C). \[ \boxed{10} \]
Was this answer helpful?
0
0
Top MHT CET Physics Questions
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is
- If $M_z$ = magnetization of a paramagnetic sample, $B$ = external magnetic field, $T$ = absolute temperature, $C$ = curie constant then according to Curie�s law in magnetism, the correct relation is
- In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $'t'$ second. The frequency of vibration of air column is
- In a parallel plate capacitor, the capacity increases if
View More Questions
Top MHT CET Keplers Laws Questions
- What is the ratio of escape velocity to orbital velocity?
- The period of revolution of planet A around the sun is 8 times that of \( B \). The distance of \( A \) from the sun is how many times greater than that of \( B \) from the sun?
- If the horizontal velocity given to a satellite is greater than critical velocity but less than the escape velocity at the height, then the satellite will
- The period of revolution of planet A around the sun is 8 times that of planet B. How many times the distance of A from the sun is greater than that of B from the sun?
- The time period of a satellite of earth is $5\text{ hours}$. If the separation between the earth and the satellite is increased to four times the previous value, the new time period of the satellite will be
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions