A mass M is divided into two parts xM and (1 | vedclass

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

Question

(A) The gravitational force $F$ between two masses $m_1 = xM$ and $m_2 = (1 - x)M$ separated by a distance $r$ is given by:$F = \frac{G m_1 m_2}{r^2}

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(A) The gravitational force $F$ between two masses $m_1 = xM$ and $m_2 = (1 - x)M$ separated by a distance $r$ is given by:$F = \frac{G m_1 m_2}{r^2} = \frac{G (xM) ((1 - x)M)}{r^2}$$F = \frac{G M^2}{r^2} (x - x^2)$To find the value of $x$ for which $F$ is maximum,we differentiate $F$ with respect to $x$ and set it to zero:$\frac{dF}{dx} = \frac{G M^2}{r^2} \frac{d}{dx} (x - x^2) = 0$$\frac{G M^2}{r^2} (1 - 2x) = 0$Since $\frac{G M^2}{r^2} 
eq 0$,we have:$1 - 2x = 0$$2x = 1$$x = 1/2$Thus,the gravitational force is maximum when $x = 1/2$.

$A$ mass $M$ is divided into two parts $xM$ and $(1 - x)M$. For what value of $x$ is the gravitational force between them maximum for a given distance?

Similar Questions

The mass of the moon is about $1.2\%$ of the mass of the earth. Compared to the gravitational force the earth exerts on the moon,the gravitational force the moon exerts on the earth:

The distance between the centres of the moon and the earth is $D$. 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 a test mass be zero?

Four identical particles of mass $m$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is $\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{Gm^2}{L^2}$,the length of the sides of the square is

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:

Two solid spheres each of radius $R$ made of the same material are placed in contact with each other. If the gravitational force acting between them is $F$,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module