TG EAMCET 3 May 2025 Shift 2 Paper

Step 1: Displacement equations
The proton and the alpha particle both start from rest, so their displacement after some time is given by:
s=‌

1

2

at2.
Since they travel the same distance:
‌

1

2

aαtα2=‌

1

2

aptp2
This means:
aαtα2=aptp2
Step 2: Acceleration in an electric field
The acceleration of a charged particle in an electric field E is:
a=‌

qE

m

- For a proton, charge =e, mass =mp
- For an alpha particle, charge =2e, mass =4mp
So: −ap=‌

eE

mp

−aα=‌

2eE

4mp

=‌

eE

2mp

Step 3: Substitute accelerations into equation
Plug the accelerations into the earlier equation:
(‌

eE

2mp

)tα2=(‌

eE

mp

)tp2
Step 4: Solve for time ratio
Divide both sides by ‌

eE

mp

:
‌

tα2

2

=tp2
This gives:

tα2=2tp2
Taking square roots:
tα=√2tp
So,
‌

tp

tα

=‌

1

√2

or
tp:tα=1:√2