KCET · Physics · Electrostatics
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 \( \frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}=0.5 \) ?
- A \( \frac{a_{1}}{a_{2}}=0.5 \)
- B \( \frac{a_{1}}{a_{2}}=1 \)
- C \( \frac{a_{1}}{a_{2}}=2 \)
- D \( \frac{a_{1}}{a_{2}}=3 \)
Answer & Solution
Correct Answer
(C) \( \frac{a_{1}}{a_{2}}=2 \)
Step-by-step Solution
Detailed explanation
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
\( \frac{a_{1}}{a_{2}}=\frac{1}{0.5} \Rightarrow \frac{a_{1}}{a_{2}}=2 \)
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