JEE Mains · Physics · STD 11 - 3.2 motion in plane
A particle is moving with uniform speed along the circumference of a circle of radius \(R\) under the action of a central fictitious force \(F\) which is inversely proportional to \(R ^{3}\). Its time period of revolution will be given by
- A \(T \propto R ^{2}\)
- B \(T \propto R ^{\frac{3}{2}}\)
- C \(T \propto R ^{\frac{5}{2}}\)
- D \(T \propto R ^{\frac{4}{3}}\)
Answer & Solution
Correct Answer
(A) \(T \propto R ^{2}\)
Step-by-step Solution
Detailed explanation
\(F \propto \frac{1}{R^{3}}\) \(\frac{K}{R^{3}}=m \omega^{2} R\) \(\omega^{2}=\frac{K}{m} \times \frac{1}{R^{4}}\) \(\left(\frac{2 \pi}{T}\right)^{2}=\frac{K}{m} \times \frac{1}{R^{4}}\) \(T^{2} \propto R^{4}\) \(T \propto R^{2}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A Zener of breakdown voltage \(V_{z}=8\,V\) and maximum zener current, \(I _{ ZM }=10\,mA\) is subjected to an input voltage \(V _{ i }=10\,V\) with series resistance \(R=100\,\Omega\). In the given circuit \(R_{L}\) represents the variable load resistance. The ratio of maximum and minimum value of \(R_{L}\) is
JEE Mains 2022 Hard - The electrostatic force \(\left(\vec{F}_1\right)\) and magnetic force \(\left(\vec{F}_2\right)\) acting on a charge \(q\) moving with velocity \(v\) can be written _______.JEE Mains 2024 Hard
- The \(B-H\) curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with \(1000\, turns/cm\) . The current that should be passed in the solenoid to demagnetise the ferromagnet completely is
JEE Mains 2018 Medium - A spherically symmetric charge distribution is characterised by a charge density having the following variations \(\rho (r)\, = \,{\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(r < R\) \(\rho (r)\,=\,0\) for \(r\, \ge \,R\) Where \(r\) is the distance from the centre of the charge distribution \(\rho _0\) is a constant. The electric field at an internal point \((r < R)\) isJEE Mains 2014 Hard
- According to Bohr atom model, in which of the following transitions will the frequency be maximum ?JEE Mains 2021 Hard
- In a large building, there are \(15\) bulbs of \(40\ W\), \(5\) bulbs of \(100\ W, 5\) fans of \(80\ W\) and \(1\) heater of \(1\ kW\). The voltage of electric mains is \(220\ V\). The minimum capacity of the main fuse of the building will be ................ \(A\)JEE Mains 2014 Medium
More PYQs from JEE Mains
- Let \(O\) be the origin and the position vector of the point \(P\) be \(-\hat{i}-2 \hat{j}+3 \hat{k}\). If the position vectors of the points \(A , B\) and \(C\) are \(-2 \hat{i}+\hat{j}-3 \hat{k}, 2 \hat{i}+4 \hat{j}-2 \hat{k}\) and \(-4 \hat{i}+2 \hat{j}-\hat{k}\) respectively then the projection of the vector \(\overline{O P}\) on a vector perpendicular to the vectors \(\overline{A B}\) and \(\overline{A C}\) is \(......\).JEE Mains 2023 Hard
- If \(Q(0, -1, -3)\) is the image of the point \(P\) in the plane \(3x -y+4z = 2\) and \(R\) is the point \((3, -1, -2)\), then the area (in square units) of \(\Delta PQR\) isJEE Mains 2019 Hard
- If each diode has a forward bias resistance of \(25\,\Omega\) in the below circuit,Which of the following options is correct:
JEE Mains 2023 Medium - Let the vertices \(Q\) and \(R\) of the triangle \(P Q R\) lie on the line \(\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}, Q R=5\) and the coordinates of the point \(P\) be \((0,2,3)\). If the area of the triangle \(P Q R\) is \(\frac{m}{n}\) then :JEE Mains 2025 Medium
- In a Young's double slits experiment, the ratio of amplitude of light coming from slits is \(2: 1\). The ratio of the maximum to minimum intensity in the interference pattern is :JEE Mains 2023 Medium
- A gas molecule of mass \(M\) at the surface of the Earth has kinetic energy equivalent to \(0\,^oC\). If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth. (\(k_B\) is Boltzmann constant)JEE Mains 2014 Medium