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Center of Mass question

2020 · 9 Jan · Shift 2 · Q63
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Center of Mass question

2020 · 9 Jan · Shift 2 · Q63

JEE MainPhysicsCenter of MassMCQ+4 / −1
A rod of length L has non-uniform linear mass density given by ρ\rhoρ(x) = a+b(xL)2a + b{\left( {{x \over L}} \right)^2}a+b(Lx​)2, where a and b are constants and 0 ≤\le≤ x ≤\le≤ L. The value of x for the centre of mass of the rod is at :
  1. A
    32(a+b2a+b)L{3 \over 2}\left( {{{a + b} \over {2a + b}}} \right)L23​(2a+ba+b​)L
  2. B
    43(a+b2a+3b)L{4 \over 3}\left( {{{a + b} \over {2a + 3b}}} \right)L34​(2a+3ba+b​)L
  3. C
    34(2a+b3a+b)L{3 \over 4}\left( {{{2a + b} \over {3a + b}}} \right)L43​(3a+b2a+b​)L
  4. D
    32(2a+b3a+b)L{3 \over 2}\left( {{{2a + b} \over {3a + b}}} \right)L23​(3a+b2a+b​)L
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