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

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(A) \(T \propto R ^{2}\)

Step-by-step Solution

Detailed explanation

\(F \propto \frac{1}{R^{3}}\)

\(\frac{K}{R^{3}}=m \omega^{2} R\)

\(\omega^{2}=\frac{K}{m} \times \frac{1}{R^{4}}\)

\(\left(\frac{2 \pi}{T}\right)^{2}=\frac{K}{m} \times \frac{1}{R^{4}}\)

\(T^{2} \propto R^{4}\)

\(T \propto R^{2}\)

Same subject

Two cells are connected between points \(A\) and \(B\) as shown. Cell \(1\) has emf of \(12\,V\) and internal resistance of \(3\,\Omega\). Cell \(2\) has emf of \(6\,V\) and internal resistance of \(6\,\Omega\). An external resistor \(R\) of \(4\,\Omega\) is connected across \(A\) and \(B\). The current flowing through \(R\) will be \(.............A\).

JEE Mains 2023 Medium
In a uniform magnetic field, the magnetic needle has a magnetic moment \(9.85 \times 10^{-2} \,{A} / {m}^{2}\) and moment of inertia \(5 \times 10^{-6} \,{kgm}^{2}\). If it performs \(10\) complete oscillations in \(5\, seconds\) then the magnitude of the magnetic field is \(....\,mT.\) [ Take \(\pi^{2}\) as \(9.85\) ]

JEE Mains 2021 Medium
A \(2\,V\) battery is connected across \(AB\) as shown in the figure. The value of the current supplied by the battery when in one case battery's positive terminal is connected to \(A\) and in other case when positive terminal of battery is connected to \(B\) will respectively be

JEE Mains 2015 Medium
A positive point charge is released from rest at a distance \(r_0\) from a positive line charge with uniform density. The speed \((v)\) of the point charge, as a function of instantaneous distance \(r\) from line charge, is proportional to

JEE Mains 2019 Hard
If momentum \([ P ]\), area \([ A ]\) and time \([ T ]\) are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :

JEE Mains 2022 Medium
The logic gate equivalent to the given logic circuit is

JEE Mains 2019 Medium

Explore more questions on app

From JEE Mains

A body of mass \(1 kg\) begins to move under the action of a time dependent force \(\vec{F}=\left(t \hat{i}+3 t^2 \hat{ j }\right) N\). where \(\hat{i}\) and \(\hat{j}\) are the unit vectors along \(x\) and \(y\) axis. The 10.Power developed by above force, at the time \(t=2 s\). will be \(..............W\).

JEE Mains 2023 Medium
Let \(\eta_{1}\) is the efficiency of an engine at \(T _{1}=447^{\circ}\,C\) and \(T _{2}=147^{\circ}\,C\) while \(\eta_{2}\) is the efficiency at \(T _{1}=947^{\circ}\,C\) and \(T _{2}=47^{\circ}\,C\). The ratio \(\frac{\eta_{1}}{\eta_{2}}\) will be.

JEE Mains 2022 Medium
The decay constant for a radioactive nuclide is \(1.5 \times 10^{-5} s ^{-1}\). Atomic of the substance is \(60\,g\) mole \(^{-1},\left( N _{ A }=6 \times 10^{23}\right)\). The activity of \(1.0\,\mu g\) of the substance is \(.......\,\times 10^{10}\,Bq\)

JEE Mains 2023 Hard

Explore more questions on app