Question

An object is projected vertically upward with a velocity 4/3 from earth. The velocity of the object at the maximum height reached by it will be a) 2
3
b) 3
c) 2 d) zero

Answer 1

Explanation:

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11th

Physics

Gravitation

Binding Energy and Satellites

An object is projected vert...

PHYSICS

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Asked on January 17, 2020 by

Amrutha Sherab

An object is projected vertically upward from the surface of the earth of mass M with a velocity such that the maximum height reached is eight times the radius R of the earth. The speed at half the maximum height will be

MEDIUM

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ANSWER

Using energy balance we have

2

1

mv

2

=−

9R

GMm

−(−

R

GMm

)

Solving we get the relation for velocity of projection as

v

2

=

9R

16GM

Now gravitational potential difference between the point at the surface and half the maximum height is given as

−

5R

GMm

−(−

R

GMm

)=

5R

4GMm

This would be equal to the change in Kinetic energy between the same points. Thus we get

2

1

m(v

2

−v

h

2

)(here v

h

is the velocity at the height of 4R from the earth)

Thus we get

2

1

m(v

2

−v

h

2

)=

5R

4GMm

or

v

h

2

=

9R

16GM

−

5R

8GM

or

v

h

=

3

2

5R

2GM