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Gravitational Potential of a Solid Sphere

A mass of 50 ...

Question

A mass of $50 kg$ is placed at the center of a uniform spherical shell of mass $100 kg$ and radius $50 m$ . If the gravitational potential at a point, $25 m$ from the center is $V kg/m$ . The value of $V$ is:

- 60 G

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- 4 G

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- 20 G

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+ 2 G

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Solution

Step 1, Given data and related image
Mass of the shell = 100 kg
Small mass = 50 kg
It can be represented as

Step 2, Finding the value of V
We know,
Gravitational potential at point $P$ is given by :
$V_{P} = \frac{- G M_{1}}{r} + \frac{- G M_{2}}{R}$
Putting all the values
$V_{P} = \frac{- 50 G}{25} + \frac{- 100 G}{50}$
$\Rightarrow V_{P} = - 4 G$
Hence the relation is as above.

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A mass of 50 kg is placed at the center of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the center is V kg/m. The value of V is:

Step 1, Given data and related imageMass of the shell = 100 kgSmall mass = 50 kgIt can be represented as Step 2, Finding the value of VWe know,Gravitational potential at point P is given by :VP=−GM1r+−GM2RPutting all the valuesVP=−50G25+−100G50⇒VP=−4GHence the relation is as above.

A mass of $50 kg$ is placed at the center of a uniform spherical shell of mass $100 kg$ and radius $50 m$ . If the gravitational potential at a point, $25 m$ from the center is $V kg/m$ . The value of $V$ is: