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The volume of the body is 5 m^3 and mas...

The volume of the body is ` 5 m^3` and mass is `60kg` then find density of body.

Text Solution

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The correct Answer is:
A, B, C
a. `m_1` is placed at a distance x from O
If rltxlt2r`, Let's consider a thin shell of mass. ltbr. `dm=m/((4/3)pir^3)xx4/3pix^3=(mx^3)/r^3`
Thus `int dm=(mx^3)/r^3`
Then gravitatioN/Al force
`F=(Gmdm)/x^2`
`=(8(mx^3)/r^3)/x^2=(Gmx)/r^3`
`b `2rltxlt2R`, then F is due to only the sphere,
`:. F=(Gmm^1)/((x-r)^2)`
c. If xlt2R then gravitatioN/Al force is due to both sphere and shelll then
due to shell `F=(GMm^2)/((x-R)^2)`
Due to the sphere `=(gmm^1)/((x-r)^2)`
So, resultant force `e=(gmm^1)/((x-r)^2) +(GMm^1)/((x-R)^2)`
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