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Standard XII

Physics

Variation of G Due to Height and Depth

On a planet w...

Question

On a planet whose size is the same and mass four times as that of our earth, find the amount of work done to lift $3$ kg mass vertically upwards through $3$ m distance on the planet. The value of g on the surface of earth is $10$ m $s^{- 2}$

360

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560

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Solution

The correct option is A $360$ J.
Here, $R_{P} = R_{e}; M_{P} = 4 M_{e}$
$M = 3 k g; h = 3 m; g_{e} = 10 m / s^{- 2}$
On the surface of the earth,
$g_{e} = \frac{G M}{R_{e}^{2}}$
On the surface of the planet,
$g_{P} = \frac{G M_{P}}{R_{P}^{2}} = \frac{G 4 M_{e}}{R_{e}^{2}} 4 \frac{G M_{e}}{R_{e}^{2}} = 4 g_{e}$
$g_{P} = 4 \times 10 = 40 m / s^{2}$
Work done $= m g_{P} h = 3 \times 40 \times 3 = 360$ J.

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On a planet whose size is the same and mass four times as that of our earth, find the amount of work done to lift 3kg mass vertically upwards through 3m distance on the planet. The value of g on the surface of earth is 10m s−2

The correct option is A 360J.Here, RP=Re;MP=4MeM=3kg;h=3m;ge=10m/s−2On the surface of the earth,ge=GMR2eOn the surface of the planet,gP=GMPR2P=G4MeR2e4GMeR2e=4gegP=4×10=40m/s2Work done =mgPh=3×40×3=360J.

On a planet whose size is the same and mass four times as that of our earth, find the amount of work done to lift $3$ kg mass vertically upwards through $3$ m distance on the planet. The value of g on the surface of earth is $10$ m $s^{- 2}$