First slide

Gravitational field intensity

Question

A body weighs 700 gm wt on the surface of the earth. How much will it weigh on the surface of a planet whose mass is $\frac{1}{7}$ and radius is half that of the earth

Moderate

A

200 gm wt
B

400 gm wt
C

50 gm wt
D

300 gm wt

Solution

W=mg=700gwt ----(1)
We know that $g = \frac{G M}{R^{2}}$
On the planet $g_{p} = \frac{G M_{p}}{{R_{p}}^{2}} = \frac{G (M / 7)}{{(\frac{R}{2})}^{2}} = \frac{G M 4}{R^{2} 7} = \frac{4}{7} g (∵ g = \frac{G M}{R^{2}})$
Hence weight on the planet $= m g_{p} = = m \frac{4 g}{7} = 700 \times \frac{4}{7} = 400 g w t$ from (1)

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