Q158 / 180 · KCET 2014 · Physics
Two equal and opposite charges of masses \( \mathrm{m}_{1} \) and \( \mathrm{m}_{2} \) are accelerated in an uniform electric
field through the same distance. What is the ratio of their accelerations if their mi ratio of
masses is \( \frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}=0.5 \) ?
field through the same distance. What is the ratio of their accelerations if their mi ratio of
masses is \( \frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}=0.5 \) ?
- A\( \frac{a_{1}}{a_{2}}=0.5 \)
- B\( \frac{a_{1}}{a_{2}}=1 \)
- Correct answerC\( \frac{a_{1}}{a_{2}}=2 \)
- D\( \frac{a_{1}}{a_{2}}=3 \)
Solution
Since both the masses are accelerated in an uniform electric field through same distance, therefore, force acting on both
the masses is same.
We know \( F= \) ma
\( \Rightarrow F_{1}=F_{2} \Rightarrow m_{1} a_{1}=m_{2} a_{2} \Rightarrow \frac{a_{1}}{a_{2}}=\frac{m_{2}}{m_{1}} \)
Using \( \frac{m_{1}}{m_{2}}=0.5 \), we get
\( \frac{a_{1}}{a_{2}}=\frac{1}{0.5} \Rightarrow \frac{a_{1}}{a_{2}}=2 \)
the masses is same.
We know \( F= \) ma
\( \Rightarrow F_{1}=F_{2} \Rightarrow m_{1} a_{1}=m_{2} a_{2} \Rightarrow \frac{a_{1}}{a_{2}}=\frac{m_{2}}{m_{1}} \)
Using \( \frac{m_{1}}{m_{2}}=0.5 \), we get
\( \frac{a_{1}}{a_{2}}=\frac{1}{0.5} \Rightarrow \frac{a_{1}}{a_{2}}=2 \)
Hence, the correct answer is option: 'C'.