At what height from the surface of earth- the gravitational potential and the value of g are -5-4 - 107 J - kg 2 and 6 m - s 2 respectively -take the radius of earth as 6400 km -A- 1400 kmB- 2000 kmC- 1600 kmD- 2600 km

The correct option is D 2600 kmGeneral expression for gravitational potential V= GM/x Where x = distance from centre of earth V= GM/(R+h)= 5.4× 10^7 ...

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Standard XII

Physics

Newton's Law of Gravitation

At what heigh...

Question

At what height from the surface of earth, the gravitational potential and the value of g are $- 5.4 \times 10^{7} J / k g^{2}$ and $6 m / s^{2}$ respectively [take the radius of earth as 6400 km]

2600 km

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1600 km

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1400 km

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2000 km

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Solution

The correct option is A 2600 km
General expression for gravitational potential
$V = \frac{- G M}{x}$
Where x = distance from centre of earth
$V = \frac{- G M}{(R + h)} = - 5.4 \times 10^{7}$ $c d o t s (1)$
negative sign for attractive force
$g_{s u r f a c e} = \frac{G M}{(R + h)} = 6$ $\dots (2)$
By (1) and (2)
9000 K = R + h
h = 2600km

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At what height from the surface of earth, the gravitational potential and the value of g are −5.4×107 J/kg2 and 6m/s2 respectively [take the radius of earth as 6400 km]

The correct option is A 2600 kmGeneral expression for gravitational potential V=−GMx Where x = distance from centre of earth V=−GM(R+h)=−5.4×107 cdots(1) negative sign for attractive force gsurface=GM(R+h)=6 ⋯(2) By (1) and (2) 9000 K = R + h h = 2600km

At what height from the surface of earth, the gravitational potential and the value of g are $- 5.4 \times 10^{7} J / k g^{2}$ and $6 m / s^{2}$ respectively [take the radius of earth as 6400 km]