Question

A bullet is fired vertically upwards with velocity from the surface of a spherical planet. When it reaches its maximum heights, its acceleration due to the planet's gravity is th of its value at the surface of the planet. If the escape velocity from the planet is , then the value of N is (ignore energy loss due to atmosphere)

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Solution
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Correct option is A)

We know that at the surface of the earth, value of
At height above the Earth's surface, the value of acceleration due to gravity
So it is given that
When the bullet reaches maximum height, acceleration due to gravity is th of that at planet's surface. 

That implies

By conservation of mechanical energy, since velocity is zero at max height.  


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