Two stars of masses 3times10^{31} kg each,an | vedclass

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Question

(D) Let the mass of the meteorite be $m$. The distance of each star from the center of mass $O$ is $r = d/2 = (2	imes10^{11} \ m)/2 = 1	imes10^{11}

Vedclass · Accepted Answer

$2.8	imes10^5 \ m/s$

Vedclass · Answer

(D) Let the mass of the meteorite be $m$. The distance of each star from the center of mass $O$ is $r = d/2 = (2	imes10^{11} \ m)/2 = 1	imes10^{11} \ m$.The gravitational potential energy of the meteorite at point $O$ due to the two stars is $U = -\frac{GMm}{r} - \frac{GMm}{r} = -\frac{2GMm}{r}$.To escape the gravitational field,the total mechanical energy of the meteorite at $O$ must be at least zero. By the law of conservation of energy:$\frac{1}{2}mv^2 + U = 0$$\frac{1}{2}mv^2 - \frac{2GMm}{r} = 0$Solving for $v$:$v^2 = \frac{4GM}{r}$$v = \sqrt{\frac{4 	imes 6.67	imes10^{-11} 	imes 3	imes10^{31}}{1	imes10^{11}}}$$v = \sqrt{4 	imes 6.67 	imes 3 	imes 10^9}$$v = \sqrt{80.04 	imes 10^9} = \sqrt{8.004 	imes 10^{10}}$$v \approx 2.83 	imes 10^5 \ m/s$.

Column-$I$	Column-$II$
$(1)$ Value of escape velocity on the surface of the Earth	$(a)$ $2.38 \, km \, s^{-1}$
$(2)$ Value of escape velocity on the surface of the Moon	$(b)$ $7.92 \, km \, s^{-1}$
	$(c)$ $11.2 \, km \, s^{-1}$

Similar Questions

Match Column-$I$ with Column-$II$.

Column-$I$ Column-$II$

$(1)$ Value of escape velocity on the surface of the Earth $(a)$ $2.38 \, km \, s^{-1}$

$(2)$ Value of escape velocity on the surface of the Moon $(b)$ $7.92 \, km \, s^{-1}$

$(c)$ $11.2 \, km \, s^{-1}$

$A$ body is projected up with a velocity equal to $\frac{3}{4}$ of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth $= R$)

$A$ spaceship of mass $2 \times 10^4 \, kg$ is launched into a circular orbit close to the Earth's surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be $......$ (given $g = 10 \, m/s^2$ and radius of Earth $R = 6400 \, km$).

The escape velocity from the surface of the Earth is $V_e$. The escape velocity from the surface of a planet whose mass and radius are $3$ times those of the Earth will be:

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