The distance between two objects A and B is r | vedclass

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

Question

(A) According to the inverse square law,the gravitational force between $A$ and $B$ is given by:$F = G \frac{m_A m_B}{r^2}$The acceleration of object

Vedclass · Accepted Answer

$a_A / r^2$

Vedclass · Answer

(A) According to the inverse square law,the gravitational force between $A$ and $B$ is given by:$F = G \frac{m_A m_B}{r^2}$The acceleration of object $A$ is $a_A = \frac{F}{m_A} = \frac{G m_B}{r^2}$ ... $(1)$For the second case,where the force is inversely proportional to the fourth power of the distance:$F' = G \frac{m_A m_B}{r^4}$The new acceleration of object $A$ is $a_A' = \frac{F'}{m_A} = \frac{G m_B}{r^4}$Substituting the expression from equation $(1)$ into the new acceleration formula:$a_A' = \frac{1}{r^2} \left( \frac{G m_B}{r^2} \right) = \frac{a_A}{r^2}$Therefore,the acceleration of object $A$ becomes $\frac{a_A}{r^2}$.

The distance between two objects $A$ and $B$ is $r$. The gravitational force between them is inversely proportional to the square of the distance. If the gravitational force between these two objects were inversely proportional to the fourth power of the distance,find the acceleration of object $A$.

Similar Questions

$A$ black hole is a:

The distance between the centre of the moon and the earth is $D$ and the mass of the earth is $81$ times the mass of the moon. At what distance from the centre of the earth will the net gravitational force on an object be zero?

$A$ mass $M$ at rest is broken into two pieces having masses $m$ and $(M-m)$. The two masses are then separated by a distance $r$. The gravitational force between them will be maximum when the ratio of the masses $[m : (M-m)]$ of the two parts is:

There are three arrangements of three point masses (each of mass $m$). In which of the following three arrangements are they arranged in order of increasing magnitude of the net gravitational force on the point mass marked as $1$?

Find the gravitational force between two stones, each of mass $2 \,kg$ and separated by a distance $1 \,m$ in vacuum.

Vedclass Test Series

Exam Paper Generator

Online Exam Module