The figure shows the variation of the gravita | vedclass

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

Question

(A) For $r \geq R$,the gravitational acceleration is given by $a_g = \frac{GM}{r^2}$.Substituting $M = \rho \cdot \frac{4}{3} \pi R^3$,we get $a_g = \

Vedclass · Accepted Answer

$1, 2, 3, 4$

Vedclass · Answer

(A) For $r \geq R$,the gravitational acceleration is given by $a_g = \frac{GM}{r^2}$.Substituting $M = \rho \cdot \frac{4}{3} \pi R^3$,we get $a_g = \frac{G \rho \frac{4}{3} \pi R^3}{r^2} = \frac{4}{3} \pi G \rho \frac{R^3}{r^2}$.For $r \geq R$,the curves coincide if the product $\rho R^3$ is the same.Given that plots $1$ and $2$ coincide for $r \geq R_2$,it implies $\rho_1 R_1^3 = \rho_2 R_2^3$. Since $R_1  \rho_2$.Similarly,plots $3$ and $4$ coincide for $r \geq R_4$,implying $\rho_3 R_3^3 = \rho_4 R_4^3$. Since $R_3  \rho_4$.Comparing the curves at a common distance $r$,$a_g$ is higher for curves $1$ and $2$ than for $3$ and $4$,implying $\rho_1, \rho_2 > \rho_3, \rho_4$.Thus,the descending order of densities is $\rho_1 > \rho_2 > \rho_3 > \rho_4$.

Similar Questions

$A$ coin and a six-faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die is:

The motion of a particle along a straight line is described by the equation $x = 8 + 12t - t^3$,where $x$ is in $m$ and $t$ is in $s$. The retardation of the particle when its velocity becomes zero is ....... $m s^{-2}$.

For an ellipse with eccentricity $e = \frac{1}{2}$,the centre is at the origin. If one directrix is $x = 4$,then the equation of the ellipse is:

Which insecticide is lipophilic in nature?

The ratio of angular speeds of the minute hand and the hour hand of a watch is

Vedclass Test Series

Exam Paper Generator

Online Exam Module