MHT CET · Physics · Motion In Two Dimensions
A particle of mass ' \(m\) ' performs uniform circular motion of radius ' \(r\) ' with linear speed ' \(v\) ' under the application of force ' \(F\) '. If ' \(m\) ', ' \(v\) ' and ' \(r\) ' are all increased by \(20 \%\) the necessary change in force required to maintain the particle in uniform circular motion, is
- A \(12 \%\)
- B \(14 \%\)
- C \(44 \%\)
- D \(144 \%\)
Answer & Solution
Correct Answer
(C) \(44 \%\)
Step-by-step Solution
Detailed explanation
Let initial force be,
\(F_1=\frac{m^2}{r}\)
After \(20 \%\) increase in all \(\mathrm{m}, \mathrm{v}\) and r ,
\(\begin{array}{ll}
& \mathrm{F}_2=\frac{1.2 \mathrm{~m} \times(1.2 \mathrm{v})^2}{1.2 \mathrm{r}}=1.44 \frac{\mathrm{mv}^2}{\mathrm{r}}=1.44 \mathrm{~F}_1 \\
\therefore \quad & \mathrm{~F}_2-\mathrm{F}_1=0.44 \mathrm{~F}_1 \\
\therefore \quad & \frac{\mathrm{~F}_2-\mathrm{F}_1}{\mathrm{~F}_1} \times 100=44 \%
\end{array}\)
i.e., increase in force required is \(44 \%\)
\(F_1=\frac{m^2}{r}\)
After \(20 \%\) increase in all \(\mathrm{m}, \mathrm{v}\) and r ,
\(\begin{array}{ll}
& \mathrm{F}_2=\frac{1.2 \mathrm{~m} \times(1.2 \mathrm{v})^2}{1.2 \mathrm{r}}=1.44 \frac{\mathrm{mv}^2}{\mathrm{r}}=1.44 \mathrm{~F}_1 \\
\therefore \quad & \mathrm{~F}_2-\mathrm{F}_1=0.44 \mathrm{~F}_1 \\
\therefore \quad & \frac{\mathrm{~F}_2-\mathrm{F}_1}{\mathrm{~F}_1} \times 100=44 \%
\end{array}\)
i.e., increase in force required is \(44 \%\)
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