TG EAMCET 3 May 2025 Shift 1 Paper

Step 1: Use the conservation of energy
When an object moves in Earth's gravity, its total energy (kinetic plus potential) stays the same if no energy is lost.
Step 2: Write the energy equation
The equation is: ‌

1

2

mVi2−‌

GMm

R

=‌

1

2

mVf2+0
Here, Vi is the speed at the start, and Vf is the speed far away from Earth (where gravity is almost zero).
Step 3: Substitute the initial speed
The body is thrown with speed Vi=√5Ve, where Ve is escape velocity.
Step 4: Plug in values and simplify
‌‌

1

2

m(√5Ve)2−‌

gR2m

R

=‌

1

2

mVf2
‌⇒‌

5

2

mVe2−gRm=‌

1

2

mVf2
‌⇒‌

5

2

Ve2−gR=‌

1

2

Vf2
Step 5: Express gR in terms of Ve
Remember, Ve=√2gR. Square both sides to get Ve2=2gR.
So, gR=‌

Ve2

2

.
Step 6: Substitute and solve for Vf
Plug gR=‌

Ve2

2

into the previous equation:
‌‌

5

2

Ve2−‌

Ve2

2

=‌

1

2

Vf2
‌(5−1)‌

Ve2

2

=‌

1

2

Vf2
‌4‌

Ve2

2

=‌

1

2

Vf2
Multiply both sides by 2 :
4Ve2=Vf2
Take square root:
Vf=2Ve