Two particles having masses m and 4m are separated by distance l. The distance of the centre of mass from m is x1 and x2 is the distance of point at which gravitational field intensity is zero. Find the value of (x1/x2)

Question

Two particles having masses m and 4m are separated by distance l. The distance of the centre of mass from m is x1 and x2 is the distance of point at which gravitational field intensity is zero. Find the value of (x1/x2) <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-tbbk0kxlsrvr.png" /> (A) 1 (B) 2 (C) 2.4 (D) 3.6

Tardigrade Admin · Accepted Answer

x1=(4 m l/5 m)=0.8 l (G m/x22)=(4 G m/(l-x2)2) 2 x2+x2=l x2=(1/3) (x1/x2)=2.4

Q. Two particles having masses $m$ and $4 m$ are separated by distance $l .$ The distance of the centre of mass from m is $x_{1}$ and $x_{2}$ is the distance of point at which gravitational field intensity is zero. Find the value of $\frac{x _{1}}{x _{2}}$

$1$

$2$

$2.4$

$3.6$

$x_{1} = \frac{4 m l}{5 m} = 0.8 l$
$\frac{G m}{x _{2}^{2}} = \frac{4 G m}{( l - x _{2} ) ^{2}}$
$2 x_{2} + x_{2} = l$
$x_{2} = \frac{1}{3}$
$\frac{x _{1}}{x _{2}} = 2.4$

Q. Two particles having masses m and 4m are separated by distance l. The distance of the centre of mass from m is x1​ and x2​ is the distance of point at which gravitational field intensity is zero. Find the value of x2​x1​​

1

2

2.4

3.6

x1​=5m4ml​=0.8l x22​Gm​=(l−x2​)24Gm​ 2x2​+x2​=l x2​=31​ x2​x1​​=2.4

Q. Two particles having masses $m$ and $4 m$ are separated by distance $l .$ The distance of the centre of mass from m is $x_{1}$ and $x_{2}$ is the distance of point at which gravitational field intensity is zero. Find the value of $\frac{x _{1}}{x _{2}}$

$1$

$2$

$2.4$

$3.6$

$x_{1} = \frac{4 m l}{5 m} = 0.8 l$
$\frac{G m}{x _{2}^{2}} = \frac{4 G m}{( l - x _{2} ) ^{2}}$
$2 x_{2} + x_{2} = l$
$x_{2} = \frac{1}{3}$
$\frac{x _{1}}{x _{2}} = 2.4$