A satellite is launched into a circular orbit | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) According to Kepler's third law of planetary motion,the square of the time period $T$ is proportional to the cube of the orbital radius $R$,i.e.,$

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) According to Kepler's third law of planetary motion,the square of the time period $T$ is proportional to the cube of the orbital radius $R$,i.e.,$T^2 \propto R^3$.Let $T_1$ be the time period for radius $R_1 = R$ and $T_2$ be the time period for radius $R_2 = 1.02 R$.Then,$\frac{T_2}{T_1} = \left( \frac{R_2}{R_1} ight)^{3/2} = (1.02)^{3/2}$.Using the binomial approximation $(1 + x)^n \approx 1 + nx$ for small $x$:$\frac{T_2}{T_1} = (1 + 0.02)^{3/2} \approx 1 + \frac{3}{2} 	imes 0.02 = 1 + 0.03 = 1.03$.Thus,$T_2 = 1.03 T_1$.The percentage difference is given by $\frac{T_2 - T_1}{T_1} 	imes 100 = \frac{1.03 T_1 - T_1}{T_1} 	imes 100 = 0.03 	imes 100 = 3\%$.

$A$ satellite is launched into a circular orbit of radius $R$ around the Earth,while a second satellite is launched into an orbit of radius $1.02 R$. The percentage difference in the time periods of the two satellites is:

Similar Questions

$A$ small sphere carrying a charge $q$ is suspended by a string of length $L$ between two parallel plates. The time period of the pendulum is $T_0$. When the capacitor is charged,the time period changes to $T$. The ratio $T/T_0$ is equal to:

The de-Broglie wavelength of a particle moving with a velocity $2.25 \times 10^8 \, m/s$ is equal to the wavelength of a photon. The ratio of the kinetic energy of the particle to the energy of the photon is (velocity of light is $3 \times 10^8 \, m/s$):- (in $/8$)

The number of subsets of $\{1, 2, 3, \ldots, 9\}$ containing at least one odd number is

Which of the following compounds is not chiral?

Vedclass Test Series

Exam Paper Generator

Online Exam Module