A ball is dropped from a spacecraft revolving around the earth at a height of 120 km. What will happen to the ball?

It will continue to move with the same speed along the original orbit of spacecraft

It will fall down to the earth gradually

It will move with the same speed, tangentially to the spacecraft

Dimensional Formula of Gravitational Potential Energy

The dimensional formula of Gravitational Potential Energy is given by,

M¹ L² T^-2

Where,

Gravitational Potential Energy (G.P.E) = Mass × Acceleration due to gravity × Altitude . . . (1)

The dimensional formula of mass and altitude = [M¹ L⁰ T⁰] and [M⁰ L¹ T⁰] . . . . (2)

And, the dimensional formula of g = [M⁰ L¹ T^-2] . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Gravitational Potential Energy = Mass × Acceleration due to gravity × Altitude

Or, G.P.E = [M¹ L⁰ T⁰] × [M⁰ L¹ T^-2] × [M⁰ L¹ T⁰] = [M¹ L² T^-2].

Therefore, Gravitational Potential Energy is dimensionally represented as [M¹ L² T^-2].

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