Question

Weight of a body of mass m decreases by 1% when
it is raised to height h above the earth's surface.
If the body is taken to a depth h in a mine, then
in its weight will
(1) decrease by 0.5% (2) decrease by 2%
(3) increase by 0.5% (4) increase by 1%

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Answer 1

Dear Student,

◆ Answer -

(1) decrease by 0.5%

● Explanation -

Formulas used here are considering R >>> h.

Acceleration due to gravity at height h,

gh = g(1-2h/R)

Reduction in weight at height h is given by -

∆Wh = m(g-gh)

∆Wh = m[g - g(1-2h/R)]

∆Wh = 2mgh/R ...(1)

Acceleration due to gravieight at depth d is,

gd = g(1-h/R)

Reduction in weight at depth d is given by -

∆Wd = m(g-gd)

∆Wd = m[g - g(1-h/R)]

∆Wd = mgh/R ...(2)

From (1) & (2),

∆Wd = 1/2 ∆Wh

Therefore, when weight of body decreases by 1 % at height h, it will decease to 1/2 × 1 = 0.5 % at same depth.

Hope this helps you...