A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere (you may take G = 6.67 × 10-11 Nm2 kg-2

Question

A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere (you may take G = 6.67 × 10-11 Nm2 kg-2 (A) 13.34 × 10-10 J (B) 3.33 × 10-10 J (C) 6.67 × 10-9 J (D) 6.67 × 10-10 J

Tardigrade Admin · Accepted Answer

Ui = -(GMm/r) Ui = -(6.67 × 10-11 × 100 × 10-2/0.1) Ui = (6.67 × 10-11/0.1) = - 6.67 × 10-10 J We know ∴ W = Δ U = Uf - Ui (∵ Uf = 0) ∴ W = - Ui = 6.67 × 10-10 J

Q. A particle of mass $10 g$ is kept on the surface of a uniform sphere of mass $100 k g$ and radius $10 c m$ . Find the work to be done against the gravitational force between them, to take the particle far away from the sphere (you may take $G = 6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}$

$13.34 \times 1 0^{- 10} J$

$3.33 \times 1 0^{- 10} J$

$6.67 \times 1 0^{- 9} J$

$6.67 \times 1 0^{- 10} J$

$U_{i} = - \frac{GM m}{r}$
$U_{i} = - \frac{6.67 \times 1 0 ^{- 11} \times 100 \times 1 0 ^{- 2}}{0.1}$
$U_{i} = \frac{6.67 \times 1 0 ^{- 11}}{0.1}$
$= - 6.67 \times 1 0^{- 10} J$
We know
$∴ W = Δ U$
$= U_{f} - U_{i} (∵ U_{f} = 0)$
$∴ W = - U_{i} = 6.67 \times 1 0^{- 10} J$

Q. A particle of mass 10g is kept on the surface of a uniform sphere of mass 100kg and radius 10cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere (you may take G=6.67×10−11Nm2kg−2

13.34×10−10J

3.33×10−10J

6.67×10−9J

6.67×10−10J