AP EAMCET Engineering 2018 Apr 22 Shift 2 Paper

The escape velocity is given by,
VEscape=√

2GM

R

Consider, if the object is thrown with a speed of x then the object rises up to height of h, then by using the conservation of energy we obtain.
The below figure represent the required diagram.

1

2

m(xVEscape)2−

GMm

R

=0−

GMm

R+h

1

2

m(xVEscape)2=

GMm

R

−

GMm

R+h

1

2

x2(√

2GM

R

)2=

GM

R

−

GM

R+h

1

2

x2

2GM

R

=

GM

R

−

GM

R+h

x2

R

=

1

R

−

1

R+h

x2=1−

R

R+h

h=

Rx2

1−x2

Thus no option is correct.