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An object weighs 100N on the earth's surface. Find its weight at a point P with o...


Question

An object weighs 100N on the earth's surface. Find its weight at a point P with orbital radius 2R. [g =10Nkg\(^{-1}\)]

Options

A) 40.0N

B) 35.0N

C) 25.0N

D) 20.0N

The correct answer is C.

Explanation:

Weight, W = mg, W = 100N, g = 10Nkg\(^{-1}\)
\(m = \cfrac{W}{g} = \cfrac{100}{10} = 10\)kg
\(g = \cfrac{GM}{R^2};\)
\(g_1R_1^2 = g_2R_2^2\)
\(R_2 = 2R; g = \cfrac{10R^2}{4R^2} = 2.5\)Nkg\(^{-1}\)
Weight of object at 2;
\(W = mg = 10 \times 2.5 = 25N\)

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Dicussion (1)

  • Weight, W = mg, W = 100N, g = 10Nkg\(^{-1}\)
    \(m = \cfrac{W}{g} = \cfrac{100}{10} = 10\)kg
    \(g = \cfrac{GM}{R^2};\)
    \(g_1R_1^2 = g_2R_2^2\)
    \(R_2 = 2R; g = \cfrac{10R^2}{4R^2} = 2.5\)Nkg\(^{-1}\)
    Weight of object at 2;
    \(W = mg = 10 \times 2.5 = 25N\)