JEE Main 2015 (Offline) | Gravitation Question 165 | Physics

From a solid sphere of mass $$M$$ and radius $$R,$$ a spherical portion of radius $$R/2$$ is removed, as shown in the figure. Taking gravitational potential $$V=0$$ at $$r = \infty ,$$ the potential at the center of the cavity thus formed is:
($$G=gravitational $$ $$constant$$) JEE Main 2015 (Offline) Physics - Gravitation Question 163 English

JEE Main 2015 (Offline) Physics - Gravitation Question 163 English

$${{ - 2GM} \over {3R}}$$

$${{ - 2GM} \over R}$$

$${{ - GM} \over {2R}}$$

$${{ - GM} \over R}$$

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)

-1

Four particles, each of mass $$M$$ and equidistant from each other, move along a circle of radius $$R$$ under the action of their mutual gravitational attraction. The speed of each particle is :

$$\sqrt {{{GM} \over R}} $$

$$\sqrt {2\sqrt 2 {{GM} \over R}} $$

$$\sqrt {{{GM} \over R}\left( {1 + 2\sqrt 2 } \right)} $$

$${1 \over 2}\sqrt {{{GM} \over R}\left( {1 + 2\sqrt 2 } \right)} $$

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

-1

What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and radius $$R$$ in a circular orbit at an altitude of $$2R$$?

$${{5GmM} \over {6R}}$$

$${{2GmM} \over {3R}}$$

$${{GmM} \over {2R}}$$

$${{GmM} \over {3R}}$$

AIEEE 2012

MCQ (Single Correct Answer)

-1

The mass of a spaceship is $$1000$$ $$kg.$$ It is to be launched from the earth's surface out into free space. The value of $$g$$ and $$R$$ (radius of earth ) are $$10\,m/{s^2}$$ and $$6400$$ $$km$$ respectively. The required energy for this work will be:

$$6.4 \times {10^{11}}\,$$ Joules

$$6.4 \times {10^8}\,$$ Joules

$$6.4 \times {10^9}\,$$ Joules

$$6.4 \times {10^{10}}\,$$ Joules

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