In planetary motion,the areal velocity of the | vedclass

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

Question

(C) The areal velocity $\frac{dA}{dt}$ is defined as the rate at which the area is swept by the position vector of the planet.Given that $\frac{dA}{dt

Vedclass · Accepted Answer

$\frac{dA}{dt} \propto \omega r^2$

Vedclass · Answer

(C) The areal velocity $\frac{dA}{dt}$ is defined as the rate at which the area is swept by the position vector of the planet.Given that $\frac{dA}{dt}$ depends on angular velocity $\omega$ and distance $r$,we can write: $\frac{dA}{dt} = K \omega^a r^b$.The dimensional formula for areal velocity $\frac{dA}{dt}$ is $[L^2 T^{-1}]$.The dimensional formula for angular velocity $\omega$ is $[T^{-1}]$ and for distance $r$ is $[L]$.Substituting these into the equation: $[L^2 T^{-1}] = [T^{-1}]^a [L]^b$.Comparing the exponents of $L$ and $T$ on both sides:For $T$: $-a = -1 \Rightarrow a = 1$.For $L$: $b = 2$.Therefore,the relation is $\frac{dA}{dt} \propto \omega r^2$.

In planetary motion,the areal velocity of the position vector of a planet depends on the angular velocity $\omega$ and the distance of the planet from the sun $r$. The correct relation for areal velocity is:

Similar Questions

Identify the odd one out.

Let $a \neq 0$ and $p(x)$ be a polynomial of degree greater than $2$. If $p(x)$ leaves remainders $a$ and $-a$ when divided respectively by $x+a$ and $x-a$,then the remainder when $p(x)$ is divided by $x^2-a^2$ is:

$A$ metal $M$ which is not affected by strong acids like conc. $HNO_3$,conc. $H_2SO_4$ and conc. solutions of alkalies like $NaOH$,$KOH$ forms $MCl_3$ which finds use for toning in photography. The metal $M$ is

$A$ bag $X$ contains $2$ white and $3$ black balls and another bag $Y$ contains $4$ white and $2$ black balls. One bag is selected at random and a ball is drawn from it. Then, the probability for the ball chosen to be white is:

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

Vedclass Test Series

Exam Paper Generator

Online Exam Module