KCET · Physics · Gravitation
Earth is moving around the sun in elliptical orbit as shown. The ratio of \(O B\) and \(O A\) is \(R\). Then the ratio of Earth's velocities at \(A\) and \(B\) is
- A \(R^{-1}\)
- B \(\sqrt{R}\)
- C \(R\)
- D \(R^{2 / 3}\)
Answer & Solution
Correct Answer
(C) \(R\)
Step-by-step Solution
Detailed explanation
In central force motion, the angular momentum of body remains conserved.
i.e., Angular momentum,
\(L=r \times p=m v r\)
[at minor and major axis \(\mathbf{v}\) and \(\vec{r}\) are perpendicular]
So, if \(v_{1}\) and \(v_{2}\) be the speed of earth at \(A\) and \(B\), respectively
Then, \(\quad m v_{1} r_{1}=m v_{2} r_{2}\)
\(\Rightarrow \frac{v_{1}}{v_{2}}=\frac{r_{2}}{r_{1}}=\frac{O B}{O A} \Rightarrow \frac{v_{1}}{v_{2}}=R\)
So, option (c) is correct.
i.e., Angular momentum,
\(L=r \times p=m v r\)
[at minor and major axis \(\mathbf{v}\) and \(\vec{r}\) are perpendicular]
So, if \(v_{1}\) and \(v_{2}\) be the speed of earth at \(A\) and \(B\), respectively
Then, \(\quad m v_{1} r_{1}=m v_{2} r_{2}\)
\(\Rightarrow \frac{v_{1}}{v_{2}}=\frac{r_{2}}{r_{1}}=\frac{O B}{O A} \Rightarrow \frac{v_{1}}{v_{2}}=R\)
So, option (c) is correct.
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
- Identify the logic operation performed by the circuit given here.
KCET 2010 Easy - A solenoid of length \(50 \mathrm{~cm}\) having 100 turns carries a current of \(2.5 \mathrm{~A}\). The magnetic field at one end of the solenoid isKCET 2022 Easy
- The de Broglie wavelength of an electron accelerated to a potential of \( 400 \mathrm{~V} \) is approximatelyKCET 2016 Easy
- When electron jumps from \( n=4 \) level to \( n=1 \) level, the angular momentum of electron
changes byKCET 2016 Easy - A body of mass \( 50 \mathrm{~kg} \), is suspended using a spring balance inside a lift at rest. If the lift starts
falling freely, the reading of the spring balance isKCET 2017 Easy - The maximum height attained by a projectile when thrown at an angle \(\theta\) with the horizontal is found to be half the horizontal range. Then \(\theta\) is equal toKCET 2007 Easy
More PYQs from KCET
- In \(C _4\) plants, \(C _3\) cycle takes place inKCET 2020 Medium
- Given: \( E_{M n^{+7}}^{0} \mid M n^{+2}=1.5 \mathrm{~V} \) and \( E_{M n^{+4}}^{0} \mid M n^{+2}=1.2 \mathrm{~V} \), then \( E_{M n^{+7}}^{0} \mid M n^{+4} \) isKCET 2019 Easy
- Sertoli cells are nourshing cells in the testis. They also secrete a hormone. Identify the same.KCET 2005 Hard
- From the following pedigree chart of a family, one can make an analysis that
KCET 2016 Hard - All capacitors used in the diagram are identical and each is of capacitance C. Then the effective capacitance between the point \(A\) and \(B\) is
KCET 2010 Medium - In the ionic equation
\(-\mathrm{BiO}_{3}^{-}+6 \mathrm{H}^{+}+x e^{-} \longrightarrow \mathrm{Bi}^{3+}+3 \mathrm{H}_{2} \mathrm{O}, \quad\) the values of \(x\) isKCET 2007 Easy