Two bodies of mass 100 kg and 10^4 kg are l | vedclass

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

Question

(C) Let the distance from the $100 \ kg$ mass where the gravitational field intensity is zero be $x$. At this point,the gravitational field due to bot

Vedclass · Accepted Answer

$\frac{1}{11} \ m$

Vedclass · Answer

(C) Let the distance from the $100 \ kg$ mass where the gravitational field intensity is zero be $x$. At this point,the gravitational field due to both masses must be equal in magnitude and opposite in direction. Let $m_1 = 100 \ kg$ and $m_2 = 10^4 \ kg$. The distance between them is $d = 1 \ m$. The condition for zero gravitational field is: $\frac{G m_1}{x^2} = \frac{G m_2}{(d - x)^2}$ Taking the square root on both sides: $\frac{\sqrt{m_1}}{x} = \frac{\sqrt{m_2}}{d - x}$ Rearranging for $x$: $x = \frac{d \sqrt{m_1}}{\sqrt{m_1} + \sqrt{m_2}}$ Substituting the values: $x = \frac{1 	imes \sqrt{100}}{\sqrt{100} + \sqrt{10^4}} = \frac{10}{10 + 100} = \frac{10}{110} = \frac{1}{11} \ m$.

Two bodies of mass $100 \ kg$ and $10^4 \ kg$ are lying one meter apart. At what distance from the $100 \ kg$ body will the intensity of the gravitational field be zero?

Similar Questions

$3$ particles each of mass $m$ are kept at the vertices of an equilateral triangle of side $L$. The gravitational field at the centre due to these particles is

$A$ uniform sphere has radius $R$ and mass $M$. The magnitude of the gravitational field at distances $r_1$ and $r_2$ from the centre of the sphere are $E_1$ and $E_2$ respectively. The ratio $E_1: E_2$ is ($r_1 > R$ and $r_2 < R$).

The magnitude of the gravitational field at distances $r_1$ and $r_2$ from the center of a uniform sphere of radius $R$ and mass $M$ are $F_1$ and $F_2$ respectively. The ratio $(F_1 / F_2)$ will be (if $r_1 > R$ and $r_2 < R$):

If the distance between the centres of Earth and Moon is $D$ and the mass of Earth is $81$ times that of the Moon,at what distance from the centre of Earth will the gravitational field be zero?

The gravitational force on a body of mass $1.5 \,kg$ situated at a point is $45 \,N$. The gravitational field intensity at that point is ......... $N/kg$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module