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 them

Question

Verified by Toppr

Answer 1

To take the particle far away from the sphere implies the gravitational potential is zero at that point, i.e. distance is infinite.
So, the work done is change in gravitational potential.
$W = δ U = 0 - (- \frac{G M m}{r}) = \frac{G M m}{r}$
$W = \frac{6 . 6 7 \times 1 0 ^{- 11} \times 1 0 0 \times 0 . 0 1}{0 . 1} = 6.67 \times 1 0^{- 10} J$
Option D.

Answer 2

To take the particle far away from the sphere implies the gravitational potential is zero at that point, i.e. distance is infinite.
So, the work done is change in gravitational potential.

W = δ U = 0 - (- \frac{G M m}{r}) = \frac{G M m}{r}

W = \frac{6 . 6 7 \times 1 0 ^{- 11} \times 1 0 0 \times 0 . 0 1}{0 . 1} = 6.67 \times 1 0^{- 10} J

Option D.

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 them

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

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

$6.67 \times 1 0^{- 11} J$

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

A particle of mass $m$ is located outside a uniform sphere of mass $M$ at a distance $r$ from its centre. Find the potential energy of gravitational interaction of the particle and the sphere.

A sphere of mass $50 k g$ is attached by a second sphere of mass $90 k g$ with a force equal to a weight of $0.5 m g$ and their centres are $20 c m$ apart. The gravitational constant is.

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

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 done against the gravitational force between them to take the particle far away from the sphere.

A dense sphere of mass $M$ is placed at the centre of a circle of radius $R$ . Find the work done, when a particle of mass $m$ is brought from A to B along a circle as shown in the figure.

Revise with Concepts

Gravitational Potential

Gravitational Potential Energy

Gravitational Potential Energy- Medium

Potential Energy Between Two Point Masses and System of Point Masses

Changing Configuration of a System

Gravitational Potential Energy - L2

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 them

13.34×10−10J

3.33×10−10J

6.67×10−11J

6.67×10−10J

To take the particle far away from the sphere implies the gravitational potential is zero at that point, i.e. distance is infinite. So, the work done is change in gravitational potential. W=δU=0−(−rGMm​)=rGMm​ W=0.16.67×10−11×100×0.01​=6.67×10−10J Option D.

A particle of mass m is located outside a uniform sphere of mass M at a distance r from its centre. Find the potential energy of gravitational interaction of the particle and the sphere.

A sphere of mass 50kg is attached by a second sphere of mass 90kg with a force equal to a weight of 0.5mg and their centres are 20cm apart. The gravitational constant is.

A particle of mass 10gm is kept on the surface of a uniform sphere of mass 100kg and radius 10cm. Find the work done against the gravitational force between them, to take the particle far away from the sphere. (G=6.67×10−11Nm2/Kg2)

A particle of mass 10g is kept on the surface of a uniform sphere of mass 100kg and radius 10cm. Find the work done against the gravitational force between them to take the particle far away from the sphere.

A dense sphere of mass M is placed at the centre of a circle of radius R. Find the work done, when a particle of mass m is brought from A to B along a circle as shown in the figure.

Revise with Concepts

Gravitational Potential

Gravitational Potential Energy

Gravitational Potential Energy- Medium

Potential Energy Between Two Point Masses and System of Point Masses

Changing Configuration of a System

Gravitational Potential Energy - L2

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 them

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

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

$6.67 \times 1 0^{- 11} J$

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

A particle of mass $m$ is located outside a uniform sphere of mass $M$ at a distance $r$ from its centre. Find the potential energy of gravitational interaction of the particle and the sphere.

A sphere of mass $50 k g$ is attached by a second sphere of mass $90 k g$ with a force equal to a weight of $0.5 m g$ and their centres are $20 c m$ apart. The gravitational constant is.

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

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 done against the gravitational force between them to take the particle far away from the sphere.

A dense sphere of mass $M$ is placed at the centre of a circle of radius $R$ . Find the work done, when a particle of mass $m$ is brought from A to B along a circle as shown in the figure.