Question

93. 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 x 10" N /kg)
(a) 6.67 x 10
(c) 13.34 x 10-J
(b) 6.67 * 10-
(d) 3.33 x 10-10​

Answer 1

Work done,

W=?

U=Uf-Ut=0-[GMm/R]

W=6.67×10^(-11)×100/0.1×10/1000

=6.67×10^(-10)j

Answer 2

The work done against the gravitational force between them to take  the particle far away from the sphere  $6.67\times 10^{-10}\ J$.

Explanation:

Given that,

Mass of a particle, m = 10 g = 0.01 kg

Mass of uniform sphere, M = 100 cm

Radius of sphere, R = 10 cm = 0.1 m

We need to find the work to be done against the gravitational force between them to take  the particle far away from the sphere.

Work done = change in potential energy

The final potential energy will be zero as the particle is taken far away from the sphere.

So,

$W=\Delta U\\\\W=(U_f-U_i)\\\\W=-U_i\\\\W=\dfrac{GmM}{R}\\\\W=\dfrac{6.67\times 10^{-11}\times 0.01\times 100}{0.1}\\\\W=6.67\times 10^{-10}\ J$

So, the work done against the gravitational force between them to take  the particle far away from the sphere  $6.67\times 10^{-10}\ J$.

Learn more,

Gravitational force

https://brainly.in/question/8092732