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Question

# A straight rod of length L extends from x=0 to x=L. The variation of linear mass density of the rod with x co-ordinate is λ=a0+b0x2. What is the gravitational force experienced by a point mass m at x=−a ?

A
Gm(a0a+b0L)
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B
Gm[a0(1a1a+L)+b0L+b0a2(1a1a+L)+2ab0ln(a+La)]
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C
Gm(b0L+a0a+L)
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D
None of these
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Solution

## The correct option is A Gm(a0a+b0L)NL of gravitationSmall mass dm at the centre of rod having length dxlength of rod =Lmass of rod =M K=linear mass densityK=a0+b0x2L→M unit length →MLdx→MLdx, dm→kdx.....DF=Gm(dm)x2;df=GM(kdx)x2dF=Gm(a0+b0x2)x2dxby in integration from x=1 to x=aM∫df=Gm∫a+La(a0x2+b0)dxF=Gm[−ax+bx]a+LaF=Gm(b0L+a0a+L)

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